2tan (problem 3.3.2)

Time bar (total: 8.4s)

start0.0ms (0%)

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

analyze36.0ms (0.4%)

Memory
-12.6MiB live, 32.8MiB allocated; 8ms 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)

sample4.5s (53.8%)

Memory
181.6MiB live, 4 338.1MiB allocated; 2.0s collecting garbage
Samples
1.9s25 823×0invalid
1.4s5 613×1valid
161.0ms2 643×0valid
Precisions
Click to see histograms. Total time spent on operations: 2.3s
ival-tan: 1.3s (56% of total)
ival-fabs: 226.0ms (9.7% of total)
ival-mult!: 216.0ms (9.3% of total)
adjust: 153.0ms (6.6% of total)
ival-<: 133.0ms (5.7% of total)
ival-add!: 130.0ms (5.6% of total)
ival-sub!: 89.0ms (3.8% of total)
ival-and: 63.0ms (2.7% of total)
ival-assert: 14.0ms (0.6% of total)
Bogosity

preprocess47.0ms (0.6%)

Memory
-21.9MiB live, 23.2MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
02146
18442
243242
3381142
Stop Event
1×node-limit
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶61.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Compiler

Compiled 12 to 12 computations (0% saved)

series11.0ms (0.1%)

Memory
19.5MiB live, 19.5MiB 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))

rewrite195.0ms (2.3%)

Memory
46.7MiB live, 273.4MiB allocated; 46ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01961230
02011079
11698866
09699836
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
37 → 156
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 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
(/.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (tan.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (neg.f64 (tan.f64 x))))))
(/.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 (neg.f64 (+.f64 eps x))) (/.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (neg.f64 (cos.f64 (+.f64 eps x))) (/.f64 (cos.f64 x) (sin.f64 x))))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (neg.f64 (cos.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (sin.f64 x)))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (cos.f64 x)) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (cos.f64 x)))
(/.f64 (-.f64 (*.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (/.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) #s(literal 1 binary64))) (*.f64 (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))) (/.f64 (cos.f64 x) (sin.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 (-.f64 (*.f64 (sin.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (cos.f64 (+.f64 eps x)) #s(literal 1 binary64))) (*.f64 (cos.f64 (+.f64 eps x)) (/.f64 (cos.f64 x) (sin.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 x))) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) (neg.f64 (sin.f64 x)))) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) (neg.f64 (cos.f64 x))))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) (sin.f64 x))) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) (cos.f64 x)))
(/.f64 (-.f64 (*.f64 #s(literal 1 binary64) (/.f64 (cos.f64 x) (sin.f64 x))) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) #s(literal 1 binary64))) (*.f64 (/.f64 (cos.f64 (+.f64 eps x)) (sin.f64 (+.f64 eps x))) (/.f64 (cos.f64 x) (sin.f64 x))))
(/.f64 (neg.f64 (-.f64 (*.f64 (tan.f64 (+.f64 eps x)) (cos.f64 x)) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (tan.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (*.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))))
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x
eps
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(tan.f64 (+.f64 (+.f64 x (PI.f64)) (PI.f64)))
(tan.f64 (+.f64 x (PI.f64)))
(tan.f64 x)
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#s(approx (+ x eps) eps)
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#s(approx x x)
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#s(approx (tan (+ x eps)) (tan.f64 (+.f64 eps x)))
#s(approx (+ x eps) (+.f64 eps 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 eps 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 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))

eval20.0ms (0.2%)

Memory
-12.1MiB live, 32.9MiB allocated; 7ms collecting garbage
Compiler

Compiled 1 816 to 728 computations (59.9% saved)

prune69.0ms (0.8%)

Memory
-45.3MiB live, 22.5MiB allocated; 27ms collecting garbage
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New13115146
Fresh000
Picked011
Done000
Total13116147
Accuracy
100.0%
Counts
147 → 16
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.5%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
61.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
3.4%
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
3.5%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓61.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
▶60.4%
(-.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)))
60.2%
(-.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)))
▶60.3%
(-.f64 (tan.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x)) (tan.f64 x))
60.8%
(-.f64 #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))) (tan.f64 x))
60.7%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
98.8%
#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)))
▶100.0%
#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))
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))
▶99.7%
#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))
99.3%
#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))
▶98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
Compiler

Compiled 682 to 492 computations (27.9% saved)

series136.0ms (1.6%)

Memory
20.0MiB live, 205.5MiB allocated; 43ms collecting garbage
Counts
63 → 243
Calls
Call 1
Inputs
#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))
(*.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)
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(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))
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)))))
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#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (* 2/3 (pow eps 2)))))))
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#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* x (+ (* 4/3 eps) (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))
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#s(approx (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) #s(hole binary64 (+ (* 1/3 eps) (* x (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x)))))))
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (- (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2))))))) 1/6)))
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#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* 17/9 (* eps (pow x 2)))))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* 124/45 (* eps (pow x 2)))))))))
#s(approx (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) #s(hole binary64 (* x (+ (* 2/3 eps) (* (pow x 2) (+ (* 17/9 eps) (* (pow x 2) (+ (* 124/45 eps) (* 2764/945 (* eps (pow x 2)))))))))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* -2/3 x)))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* -17/9 (pow x 2)) 2/3))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -124/45 (pow x 2)) 17/9)) 2/3))))
#s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2764/945 (pow x 2)) 124/45)) 17/9)) 2/3))))
#s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) #s(hole binary64 x))
#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 (- 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 (+ 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 (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 (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* -1/6 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) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* -11/9 (pow x 2)) 1/6))))
#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) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* (pow x 2) (- (* -197/90 (pow x 2)) 11/9)) 1/6))))
#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) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -2392/945 (pow x 2)) 197/90)) 11/9)) 1/6))))
#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) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* -41/36 (pow x 2)) 1/6))))
#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) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* -1141/720 (pow x 2)) 41/36)) 1/6))))
#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) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) #s(hole binary64 (* x (- (* (pow x 2) (- (* (pow x 2) (- (* -44981/30240 (pow x 2)) 1141/720)) 41/36)) 1/6))))
#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 (* (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 (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* (pow x 2) (+ 61/720 (* 277/6048 (pow x 2))))))))))
#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 (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 (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#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 (* 2/15 (pow x 2)))))
#s(approx (+ (/ eps x) 1) #s(hole binary64 (/ eps x)))
#s(approx (+ (/ eps x) 1) #s(hole binary64 (/ (+ eps x) x)))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* (pow eps 2) x))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* eps x) (pow eps 2))))))
#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* eps x))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (+ 1 (* x (+ eps x)))))
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Calls

6 calls:

TimeVariablePointExpression
29.0ms
x
@-inf
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26.0ms
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17.0ms
eps
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13.0ms
eps
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rewrite296.0ms (3.5%)

Memory
43.3MiB live, 360.2MiB allocated; 60ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0122723614
0134320484
0831820037
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
306 → 486
Calls
Call 1
Inputs
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#s(approx (- 1 (neg (pow (tan x) 2))) #s(hole binary64 1))
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#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)))))))))
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#s(approx (pow (tan x) 2) #s(hole binary64 (pow x 2)))
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#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
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#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
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#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)))
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#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)))
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#s(approx (- 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (* (pow x 2) (+ 1 (* -1/3 (pow x 2))))))
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#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)))
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#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)))))))
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#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 (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 x)))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* 5/36 (pow x 2))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* x (+ 1/6 (* (pow x 2) (+ 5/36 (* 61/720 (pow x 2))))))))
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#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 (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)))))
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#s(approx (+ x eps) #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (+ (* 2/15 (* x x)) 1/3) (* x x)) 1) #s(hole binary64 (+ 1 (* 1/3 (pow x 2)))))
#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 (* 2/15 (pow x 2)))))
#s(approx (+ (/ eps x) 1) #s(hole binary64 (/ eps x)))
#s(approx (+ (/ eps x) 1) #s(hole binary64 (/ (+ eps x) x)))
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#s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (+ eps (* x (+ (* x (+ eps (* eps (* x (- (* 5/6 eps) (* -1/2 eps)))))) (pow eps 2))))))
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#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 (cos x) #s(hole binary64 (cos x)))
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#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))))
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#s(approx (+ 1/2 (* 1/2 (cos (* 2 x)))) #s(hole binary64 (+ 1/2 (* 1/2 (cos (* 2 x))))))
#s(approx (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x))) #s(hole binary64 (* 1/6 (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
#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 (tan (+ x eps)) #s(hole binary64 (/ (sin (+ eps x)) (cos (+ eps x)))))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
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#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 (* (+ (/ eps x) 1) x)) (tan x)) #s(hole binary64 (- (/ (sin (* x (+ 1 (/ eps x)))) (cos (* x (+ 1 (/ eps x))))) (/ (sin x) (cos x)))))
#s(approx (tan (* (+ (/ eps x) 1) x)) #s(hole binary64 (/ (sin (* x (+ 1 (/ eps x)))) (cos (* x (+ 1 (/ eps x)))))))
#s(approx (+ (/ eps x) 1) #s(hole binary64 (+ 1 (/ eps x))))
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#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 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))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (- (/ (sin (- eps (* -1 x))) (cos (- eps (* -1 x)))) (/ (sin x) (cos x)))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(hole binary64 (* eps (- 1 (* -1 (/ (pow (sin x) 2) (pow (cos x) 2)))))))
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#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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 (/ (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 eps) #s(hole binary64 (* -1 eps)))
#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)))))
#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)))))
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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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#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) eps) #s(hole binary64 (* (pow eps 4) (+ (* -1 (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x))))) (* -1 (/ (+ (* -1 (- (/ (* (+ 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))))))) (* -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))) eps))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 3) (+ (* -1 (/ (- (/ (* (+ 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)))))) eps)) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 3) (+ (* -1 (/ (- (+ (/ (* (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)))))) eps)) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) 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 3) (+ (* -1 (/ (- (+ (* -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)) (/ (* (+ 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)))))) eps)) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x)))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 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)))))) eps)) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x)))))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) #s(hole binary64 (* (pow eps 2) (+ (* -1 (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x))))) (* -1 (/ (+ (* -1 (- (/ (* (+ 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))))))) (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (* eps (cos x))))) eps))))))
#s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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 (* eps (+ (* -1 (/ (- (/ (* (+ 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)))))) eps)) (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ (* (sin x) (- (+ 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))))))) (cos x)))))))))
#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #s(hole binary64 (* -1 (* eps (+ (* -1/2 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (+ (* 1/6 (/ 1 eps)) (/ (* (sin x) (- (+ 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))))))) (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)))))
#s(approx (- (tan (* (+ (/ eps x) 1) x)) (tan x)) #s(hole binary64 (- (/ (sin (* x (- 1 (* -1 (/ eps x))))) (cos (* x (- 1 (* -1 (/ eps x)))))) (/ (sin x) (cos x)))))
#s(approx (tan (* (+ (/ eps x) 1) x)) #s(hole binary64 (/ (sin (* x (- 1 (* -1 (/ eps x))))) (cos (* x (- 1 (* -1 (/ eps x))))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(hole binary64 (* -1 (* eps (+ (* -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)))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) #s(hole binary64 (* -1 (* eps (- (* -1 (/ (* (sin x) (+ 1 (/ (pow (sin x) 2) (pow (cos x) 2)))) (cos x))) (/ 1 eps))))))
Outputs
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#s(approx (tan x) (tan.f64 x))
#s(approx (sin x) (sin.f64 x))
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#s(approx (tan (+ x eps)) (tan.f64 (-.f64 x (*.f64 #s(literal -1 binary64) eps))))
#s(approx (+ x eps) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (/.f64 x eps) #s(literal -1 binary64)))))
#s(approx (- (tan (* (+ (/ eps x) 1) x)) (tan x)) (-.f64 (tan.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 eps x))))) (tan.f64 x)))
#s(approx (tan (* (+ (/ eps x) 1) x)) (tan.f64 (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1 binary64) (/.f64 eps x))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (*.f64 #s(literal -1 binary64) (*.f64 eps (*.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x))) (/.f64 #s(literal 1 binary64) eps)))))

eval149.0ms (1.8%)

Memory
-27.1MiB live, 223.4MiB allocated; 60ms collecting garbage
Compiler

Compiled 31 836 to 5 586 computations (82.5% saved)

prune55.0ms (0.7%)

Memory
-20.3MiB live, 70.6MiB allocated; 8ms collecting garbage
Pruning

28 alts after pruning (26 fresh and 2 done)

PrunedKeptTotal
New49919518
Fresh3710
Picked415
Done011
Total50628534
Accuracy
100.0%
Counts
534 → 28
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.5%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
▶61.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
▶3.4%
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
3.5%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓61.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓60.4%
(-.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)))
60.3%
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
60.8%
(-.f64 #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))) (tan.f64 x))
60.7%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
▶100.0%
#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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) eps))
99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) #s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) (*.f64 x (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -2/3 binary64))))) #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))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps 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))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #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))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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(literal 1/3 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))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#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))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (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) (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 #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) (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) (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) (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 #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) (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 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
▶98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
▶98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
Compiler

Compiled 2 921 to 1 798 computations (38.4% saved)

series249.0ms (3%)

Memory
32.1MiB live, 258.6MiB allocated; 31ms collecting garbage
Counts
77 → 352
Calls
Call 1
Inputs
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(neg.f64 eps)
eps
(fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x)))
(/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64))))
#s(literal 1 binary64)
(neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))
(pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64))
(*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x)))
(sin.f64 x)
x
(/.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
#s(literal 2 binary64)
#s(literal -1/2 binary64)
(/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)))) (cos.f64 x))
(fma.f64 (+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x))))
(+.f64 (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)) #s(literal 1/6 binary64)))
(*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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))))
(*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)))
(neg.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
(*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps)
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x)))
(+.f64 #s(literal 1 binary64) (*.f64 eps x))
(*.f64 eps x)
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
(*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps)
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))))))))
(+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))
(fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))))))
#s(literal 1/3 binary64)
(*.f64 eps eps)
(*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))
(fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))
(*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))
#s(literal -2/3 binary64)
(*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))
(-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps)))
(*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))
#s(literal -4/3 binary64)
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64)))
(+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))
(+.f64 (+.f64 eps x) (PI.f64))
(+.f64 eps x)
(PI.f64)
(tan.f64 x)
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps))))
(+.f64 (tan.f64 x) (tan.f64 eps))
(tan.f64 eps)
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))
(*.f64 (tan.f64 x) (tan.f64 eps))
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 eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) eps) #s(hole binary64 (* eps (+ 1 (* 1/3 (pow eps 2))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))))
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Calls

6 calls:

TimeVariablePointExpression
64.0ms
x
@inf
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48.0ms
x
@-inf
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19.0ms
eps
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18.0ms
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16.0ms
eps
@-inf
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rewrite345.0ms (4.1%)

Memory
-41.2MiB live, 443.7MiB allocated; 157ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0187133479
0201530754
0865030355
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
429 → 529
Calls
Call 1
Inputs
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Outputs
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#s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x)))
#s(approx (+ (tan x) (tan eps)) (fma.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (tan.f64 x)))
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.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)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (-.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))))))) (cos.f64 x))))))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x)) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))
#s(approx (+ 1 (* eps x)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) eps)))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) eps))) eps) (*.f64 #s(literal 4/3 binary64) (*.f64 x x)))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) eps) (*.f64 #s(literal 4/3 binary64) (*.f64 x x)))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -4/3 binary64) (/.f64 (*.f64 x x) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps)) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) eps) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 x eps)) #s(literal 2/3 binary64)))))
#s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)) #s(literal 2/3 binary64)))))
#s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 4/3 binary64) x)) eps)) #s(literal 2/3 binary64)))))
#s(approx (- (tan (+ (+ (+ eps x) (PI)) (PI))) (tan x)) (-.f64 (tan.f64 (-.f64 (+.f64 x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps))) (tan.f64 x)))
#s(approx (tan (+ (+ (+ eps x) (PI)) (PI))) (tan.f64 (-.f64 (+.f64 x (*.f64 #s(literal 2 binary64) (PI.f64))) (*.f64 #s(literal -1 binary64) eps))))
#s(approx (+ (+ (+ eps x) (PI)) (PI)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (*.f64 #s(literal 2 binary64) (PI.f64))) eps)) #s(literal 1 binary64)))))
#s(approx (+ (+ eps x) (PI)) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 x (PI.f64)) eps)) #s(literal 1 binary64)))))
#s(approx (+ eps x) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64)))))

eval160.0ms (1.9%)

Memory
16.3MiB live, 147.1MiB allocated; 24ms collecting garbage
Compiler

Compiled 35 906 to 5 712 computations (84.1% saved)

prune80.0ms (1%)

Memory
-20.8MiB live, 77.7MiB allocated; 14ms collecting garbage
Pruning

35 alts after pruning (31 fresh and 4 done)

PrunedKeptTotal
New44411455
Fresh12021
Picked325
Done022
Total44835483
Accuracy
100.0%
Counts
483 → 35
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.5%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
▶61.2%
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
61.1%
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
✓3.4%
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
3.5%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓61.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓60.4%
(-.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)))
60.3%
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
60.8%
(-.f64 #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))) (tan.f64 x))
60.7%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (fma.f64 (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64))) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64))) (*.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64))))))) eps))
▶100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 (+.f64 (fma.f64 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (+.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 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) (+.f64 (fma.f64 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (+.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 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) eps))
99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) #s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) (*.f64 x (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -2/3 binary64))))) #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))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps 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))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #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))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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(literal 1/3 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))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
▶99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#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))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (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) (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 #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) (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) (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) (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 #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) (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 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
▶98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
✓98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
98.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
▶98.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
Compiler

Compiled 5 037 to 2 503 computations (50.3% saved)

series147.0ms (1.8%)

Memory
100.8MiB live, 337.9MiB allocated; 44ms collecting garbage
Counts
85 → 327
Calls
Call 1
Inputs
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(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))))
(+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
#s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))
(*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))
(+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))
(*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))
(+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))
(*.f64 #s(literal 2/15 binary64) (*.f64 eps eps))
#s(literal 2/15 binary64)
(-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))
(*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps))))))))
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)))))
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#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 1 (* 2/3 (pow eps 2))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos 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) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (* (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) eps) #s(hole binary64 (+ (* eps (+ 1 (* 1/3 (pow eps 2)))) (* x (+ (* x (+ (* eps (+ 1 (* 4/3 (pow eps 2)))) (* (pow eps 2) (* x (+ 4/3 (* 17/9 (pow eps 2))))))) (* (pow eps 2) (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) #s(hole binary64 (+ 1 (* 1/3 (pow eps 2)))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* eps (* x (+ 1 (* 2/3 (pow eps 2)))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (* 4/3 (pow eps 2))))))))))
#s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (* (sin x) (/ 1 (cos x))) 2))) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ 1 (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2))))))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* 4/3 (* (pow eps 2) x)) (* eps (+ 1 (* 2/3 (pow eps 2))))))))))
#s(approx (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) eps) 1) #s(hole binary64 (+ 1 (+ (* 1/3 (pow eps 2)) (* x (+ (* eps (+ 1 (* 2/3 (pow eps 2)))) (* x (+ (* 4/3 (pow eps 2)) (* eps (* x (+ 4/3 (* 17/9 (pow eps 2)))))))))))))
#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) #s(hole binary64 (* 1/3 eps)))
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#s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)))) #s(hole binary64 (+ (* 1/3 eps) (* x (+ 1 (+ (* 2/3 (pow eps 2)) (* 4/3 (* eps x))))))))
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Calls

6 calls:

TimeVariablePointExpression
30.0ms
eps
@-inf
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25.0ms
eps
@inf
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22.0ms
x
@inf
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19.0ms
x
@-inf
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15.0ms
eps
@0
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rewrite375.0ms (4.5%)

Memory
-19.9MiB live, 533.3MiB allocated; 181ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0173834438
0185231259
0811330449
Stop Event
1×iter-limit
1×node-limit
1×iter-limit
Counts
412 → 511
Calls
Call 1
Inputs
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Outputs
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#s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (sin x)))) (cos x)))) 1/6) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x)) (fma.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) eps) (/.f64 (*.f64 (sin.f64 x) (-.f64 (+.f64 #s(literal 1/6 binary64) (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.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)))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (-.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))))))) (cos.f64 x))))))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ 1 (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 x x)) eps))) eps) (*.f64 #s(literal 4/3 binary64) (*.f64 x x)))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) eps) (*.f64 #s(literal 4/3 binary64) (*.f64 x x)))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -4/3 binary64) (/.f64 (*.f64 x x) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 4/3 binary64) (*.f64 x x) (/.f64 x eps)) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps)))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) x (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))) eps) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))) eps) (*.f64 #s(literal -2/3 binary64) x)))))
#s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (*.f64 #s(literal -4/3 binary64) (/.f64 x eps)) #s(literal 2/3 binary64)))))
#s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal 4/3 binary64) x (/.f64 #s(literal 1 binary64) eps)) eps)) #s(literal 2/3 binary64)))))
#s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 #s(literal -1 binary64) (*.f64 (*.f64 (*.f64 eps eps) eps) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (fma.f64 #s(literal -1 binary64) (/.f64 (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 x eps)) #s(literal 1 binary64)) eps) (*.f64 #s(literal 4/3 binary64) x)) eps)) #s(literal 2/3 binary64)))))
#s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (*.f64 #s(literal -1 binary64) (*.f64 eps (fma.f64 #s(literal -1 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x)) (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))
#s(approx (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (*.f64 #s(literal -1 binary64) (*.f64 eps (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (cos.f64 x))) (/.f64 #s(literal 1 binary64) eps)))))
#s(approx (* eps (+ 1 (* (* eps eps) (+ 1/3 (* 2/15 (* eps eps)))))) (*.f64 #s(literal -1 binary64) (*.f64 (pow.f64 eps #s(literal 5 binary64)) (-.f64 (*.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/3 binary64) (/.f64 #s(literal 1 binary64) (*.f64 eps eps))) (*.f64 eps eps))) #s(literal 2/15 binary64)))))

eval132.0ms (1.6%)

Memory
-31.6MiB live, 253.8MiB allocated; 65ms collecting garbage
Compiler

Compiled 41 710 to 5 817 computations (86.1% saved)

prune72.0ms (0.9%)

Memory
39.2MiB live, 178.2MiB allocated; 12ms collecting garbage
Pruning

36 alts after pruning (29 fresh and 7 done)

PrunedKeptTotal
New4246430
Fresh32326
Picked235
Done044
Total42936465
Accuracy
100.0%
Counts
465 → 36
Alt Table
Click to see full alt table
StatusAccuracyProgram
38.5%
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
61.2%
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
61.1%
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
✓3.4%
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
3.5%
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
✓61.1%
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
✓60.4%
(-.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)))
60.3%
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
60.8%
(-.f64 #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))) (tan.f64 x))
60.7%
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
99.9%
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100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 #s(approx (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.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))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (-.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 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) #s(approx (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.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))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (-.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 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) eps))
99.6%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) #s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) (*.f64 x (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -2/3 binary64))))) #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))
99.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps 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))
99.9%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #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))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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(literal 1/3 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))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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))
99.4%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
✓99.1%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
99.3%
#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))
100.0%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (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) (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 #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) (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) (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) (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 #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) (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 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
99.7%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
✓98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
✓98.5%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
98.2%
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
98.8%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
✓98.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
98.5%
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
Compiler

Compiled 6 131 to 1 914 computations (68.8% saved)

regimes57.0ms (0.7%)

Memory
-50.1MiB live, 110.6MiB allocated; 25ms collecting garbage
Counts
52 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) 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 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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 #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x)) (tan.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
(-.f64 #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))) (tan.f64 x))
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(*.f64 #s(literal 1/6 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) #s(literal -1/2 binary64) (*.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.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 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Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)) (cos.f64 x)) #s(literal -1/2 binary64) (/.f64 (fma.f64 (+.f64 #s(approx (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.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))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (-.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 1/6 binary64)) (sin.f64 x) (*.f64 #s(literal 1/6 binary64) (*.f64 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)))) (cos.f64 x)))) #s(literal 1/6 binary64)) #s(approx (+ (+ (* (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) -1/2) (* (pow (* (sin x) (/ 1 (cos x))) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) (-.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (*.f64 #s(literal 1/6 binary64) (/.f64 (-.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))))))) (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (/.f64 (-.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)))))) (-.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 #s(approx (- 1 (neg (pow (* (sin x) (/ 1 (cos x))) 2))) (+.f64 #s(literal 1 binary64) (/.f64 (-.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))))))) (sin.f64 x)) (cos.f64 x)))) eps #s(literal 1 binary64)) (neg.f64 (pow.f64 (*.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) eps))
Calls

3 calls:

15.0ms
x
15.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
12.0ms
eps
Results
AccuracySegmentsBranch
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
100.0%1x
100.0%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes43.0ms (0.5%)

Memory
-1.4MiB live, 98.6MiB allocated; 8ms collecting garbage
Counts
47 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
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#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))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) #s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) (*.f64 x (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -2/3 binary64))))) #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)) (tan x)) (*.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (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) (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 #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) (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) (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) (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 #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) (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 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (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))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 (fma.f64 (-.f64 (fma.f64 (neg.f64 eps) (fma.f64 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (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) (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 #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) (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) (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) (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 #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) (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 (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x))) eps #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
Calls

3 calls:

14.0ms
x
14.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
11.0ms
eps
Results
AccuracySegmentsBranch
100.0%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
100.0%1x
100.0%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes75.0ms (0.9%)

Memory
-7.7MiB live, 84.6MiB allocated; 7ms collecting garbage
Counts
45 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) 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 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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 #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x)) (tan.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
(-.f64 #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))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (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))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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(literal 1/3 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)) (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)))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #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)) (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 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (fma.f64 #s(literal 2/3 binary64) (*.f64 eps 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)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 (-.f64 (*.f64 (neg.f64 eps) #s(approx (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x))) (*.f64 x (fma.f64 #s(literal -17/9 binary64) (*.f64 x x) #s(literal -2/3 binary64))))) #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))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 (-.f64 #s(approx (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) #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))
Calls

3 calls:

32.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
29.0ms
eps
11.0ms
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)

regimes52.0ms (0.6%)

Memory
21.8MiB live, 68.1MiB allocated; 4ms collecting garbage
Counts
41 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) 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 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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 #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x)) (tan.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
(-.f64 #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))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (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))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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(literal 1/3 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)) (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)))
(-.f64 (/.f64 (pow.f64 (tan.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))) (/.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)) (+.f64 (tan.f64 (+.f64 eps x)) (tan.f64 x))))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 (-.f64 (*.f64 #s(approx (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 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(literal 1/3 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))
Calls

3 calls:

29.0ms
x
10.0ms
eps
10.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
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)

regimes47.0ms (0.6%)

Memory
12.9MiB live, 65.7MiB allocated; 5ms collecting garbage
Counts
38 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) 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 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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 #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x)) (tan.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
(-.f64 #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))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (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))
(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (+.f64 (fma.f64 eps (/.f64 (*.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (pow.f64 (tan.f64 x) #s(literal 2 binary64))) eps))
Calls

3 calls:

27.0ms
eps
9.0ms
x
9.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
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)

regimes59.0ms (0.7%)

Memory
-31.5MiB live, 61.1MiB allocated; 8ms collecting garbage
Counts
35 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
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#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) 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 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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 #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x)) (tan.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
(-.f64 #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))) (tan.f64 x))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (fma.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/3 binary64) (*.f64 eps eps))) (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
(-.f64 (/.f64 #s(approx (+ (tan x) (tan eps)) (+.f64 eps (tan.f64 x))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
(-.f64 (/.f64 (+.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))) (-.f64 #s(literal 1 binary64) (*.f64 (tan.f64 x) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 2/15 binary64) (*.f64 eps eps)))))))))) (tan.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps (/.f64 (*.f64 #s(approx (- 1 (neg (pow (tan x) 2))) #s(literal 1 binary64)) (sin.f64 x)) (cos.f64 x)) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

24.0ms
eps
23.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
9.0ms
x
Results
AccuracySegmentsBranch
99.4%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.4%1x
99.4%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes42.0ms (0.5%)

Memory
8.8MiB live, 55.1MiB allocated; 3ms collecting garbage
Counts
30 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) 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 #s(approx (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos 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 #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 x x))))) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 x (PI.f64)) eps)) (tan.f64 x))
(-.f64 (tan.f64 (+.f64 (+.f64 (+.f64 eps x) (PI.f64)) (PI.f64))) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (-.f64 (/.f64 eps x) #s(literal -1 binary64)) x)) (tan.f64 x))
(-.f64 (tan.f64 (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x)) (tan.f64 x))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (tan.f64 x) (tan.f64 (+.f64 eps x)))) (tan.f64 (+.f64 eps x)))
(-.f64 #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))) (tan.f64 x))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 (-.f64 (fma.f64 eps #s(approx (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) x) #s(literal 1 binary64)) (neg.f64 (pow.f64 (tan.f64 x) #s(literal 2 binary64)))) eps))
Calls

3 calls:

25.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms
x
7.0ms
eps
Results
AccuracySegmentsBranch
99.3%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.3%1x
99.3%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes36.0ms (0.4%)

Memory
-4.8MiB live, 43.0MiB allocated; 8ms collecting garbage
Counts
20 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
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#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
Outputs
#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))
Calls

3 calls:

24.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
5.0ms
eps
5.0ms
x
Results
AccuracySegmentsBranch
99.3%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
99.3%1x
99.3%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes16.0ms (0.2%)

Memory
38.2MiB live, 38.1MiB allocated; 0ms collecting garbage
Counts
18 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (+.f64 eps x)))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (tan eps) (*.f64 eps (+.f64 #s(literal 1 binary64) (*.f64 (*.f64 eps eps) (-.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -2/15 binary64) (*.f64 eps eps))))))))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) #s(approx (+ (* 1/3 (* eps eps)) (* x (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))))) (fma.f64 eps (+.f64 x (*.f64 eps (+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal 4/3 binary64) (*.f64 x x))))) (*.f64 x x))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 eps (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps)))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x #s(approx (+ (* eps (- 1 (* -2/3 (* eps eps)))) (* x (- 1 (* -4/3 (* eps eps))))) (*.f64 (*.f64 (*.f64 eps eps) eps) (+.f64 #s(literal 2/3 binary64) (*.f64 #s(literal 4/3 binary64) (/.f64 x eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (tan.f64 eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps #s(approx (- 1 (* -2/3 (* eps eps))) (*.f64 #s(literal 2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x #s(approx (- 1 (* -4/3 (* eps eps))) (*.f64 #s(literal 4/3 binary64) (*.f64 eps eps))))))))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/3 binary64) (*.f64 eps eps) (*.f64 x (fma.f64 eps (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -2/3 binary64) (*.f64 eps eps))) (*.f64 x (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -4/3 binary64) (*.f64 eps eps))))))))) 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)))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) (+.f64 eps (*.f64 x (fma.f64 eps x (*.f64 eps eps))))))
Calls

3 calls:

5.0ms
x
5.0ms
eps
5.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
Results
AccuracySegmentsBranch
98.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.8%1x
98.8%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes31.0ms (0.4%)

Memory
-23.3MiB live, 20.7MiB allocated; 15ms collecting garbage
Counts
5 → 1
Calls
Call 1
Inputs
#s(approx (- (tan (+ x eps)) (tan x)) #s(approx (* (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) eps) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 eps x))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* (- (* (- (- (* (neg eps) (+ (* (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)) -1/2) (/ (+ (* (+ (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x)))))))) 1/6) (sin x)) (* 1/6 (* (- 1 (neg (pow (tan x) 2))) (sin x)))) (cos x)))) 1/6) (+ (+ (* (- 1 (neg (pow (tan x) 2))) -1/2) (* (pow (tan x) 2) 1/6)) (neg (* (- 1/2 (* 1/2 (cos (* 2 x)))) (/ (- 1 (neg (pow (tan x) 2))) (+ 1/2 (* 1/2 (cos (* 2 x))))))))) eps) (neg (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x)))) eps) 1) (neg (pow (tan x) 2))) (-.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/3 binary64) (*.f64 eps eps)))) eps))
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) #s(approx (+ 1 (* eps x)) (*.f64 x (+.f64 eps (/.f64 #s(literal 1 binary64) x))))) eps))
Outputs
#s(approx (- (tan (+ x eps)) (tan x)) (*.f64 #s(approx (- (+ (* eps (/ (* (- 1 (neg (pow (tan x) 2))) (sin x)) (cos x))) 1) (neg (pow (tan x) 2))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 eps x)))) eps))
Calls

3 calls:

2.0ms
eps
2.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.0ms
x
Results
AccuracySegmentsBranch
98.8%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.8%1x
98.8%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

regimes4.0ms (0%)

Memory
14.2MiB live, 14.2MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0.1%)

Threshold costs -0b (-0.1%)

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

3 calls:

1.0ms
(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.0ms
x
1.0ms
eps
Results
AccuracySegmentsBranch
98.5%1(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
98.5%1x
98.5%1eps
Compiler

Compiled 8 to 10 computations (-25% saved)

derivations689.0ms (8.2%)

Memory
-2.3MiB live, 839.4MiB allocated; 210ms collecting garbage
Stop Event
1×fuel
Compiler

Compiled 633 to 183 computations (71.1% saved)

preprocess141.0ms (1.7%)

Memory
-27.9MiB live, 281.6MiB allocated; 109ms collecting garbage
Compiler

Compiled 667 to 213 computations (68.1% saved)

end0.0ms (0%)

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

Profiling

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