Metrics for 2sin (example 3.3)

start0.0ms (0%)

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

analyze28.0ms (0.6%)

Memory

-5.9MiB live, 10.5MiB allocated; 1ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
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)

sample3.3s (73.2%)

Memory

-39.0MiB live, 1 198.0MiB allocated; 234ms collecting garbage

Samples

1.7s	25 833×	74	invalid
411.0ms	5 111×	148	valid
189.0ms	3 145×	74	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-sin: 512.0ms (40.5% of total)

ival-fabs: 209.0ms (16.5% of total)

ival-<: 122.0ms (9.7% of total)

ival-mult!: 115.0ms (9.1% of total)

ival-add!: 110.0ms (8.7% of total)

ival-sub!: 77.0ms (6.1% of total)

ival-and: 60.0ms (4.7% of total)

adjust: 45.0ms (3.6% of total)

ival-assert: 13.0ms (1% of total)

Bogosity

explain86.0ms (1.9%)

Memory

-3.4MiB live, 37.2MiB allocated; 2ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
220	1	(-5.877306765637089e-224 3.799390028028178e-226)	10	(-1.7894275301958226e-32 3.241215919865014e-34)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	0	-	0	-	`eps`
0	0	-	0	-	`(+.f64 x eps)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	211	15

Confusion

	Predicted +	Predicted -
+	210	10
-	1	35

Precision

0.995260663507109

Recall

0.9545454545454546

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	210	10	0
-	1	5	30

Precision?

0.9734513274336283

Recall?

1.0

Freqs

test

number	freq
0	45
1	211

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

21.0ms	310×	148	valid
16.0ms	6×	2368	valid
8.0ms	196×	74	valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-sin: 25.0ms (82.7% of total)

ival-sub!: 2.0ms (6.6% of total)

ival-add!: 2.0ms (6.6% of total)

adjust: 1.0ms (3.3% of total)

preprocess85.0ms (1.9%)

Memory

6.4MiB live, 6.4MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	50
1	25	50
2	32	50
3	40	50
4	53	50
5	81	50
6	140	50
7	385	50
8	1451	50
9	5230	50
0	6	7
0	10	7
1	11	7
0	11	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Outputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.8%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

series10.0ms (0.2%)

Memory

-5.2MiB live, 2.4MiB allocated; 0ms collecting garbage

Counts

6 → 36

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (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 (sin x) #s(hole binary64 x))
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))
1.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin (+ x eps)) (+ x eps) x eps (sin x))

rewrite128.0ms (2.9%)

Memory

7.5MiB live, 45.5MiB allocated; 7ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	538
0	155	526
1	931	520
0	8567	489

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

42 → 105

Calls

Call 1

Inputs
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
(sin.f64 (+.f64 x eps))
(+.f64 x eps)
x
eps
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin eps)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (cos eps)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (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 (sin x) #s(hole binary64 x))
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (+ eps x))))
#s(approx (+ x eps) #s(hole binary64 x))
#s(approx (+ x eps) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- eps (* -1 x)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin x)))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (cos x)))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))))
#s(approx (sin (+ x eps)) #s(hole binary64 (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ x eps) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (sin (+ x eps)) #s(hole binary64 (sin (- x (* -1 eps)))))
#s(approx (+ x eps) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))

Outputs
(.f64 (.f64 #s(literal 2 binary64) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))))
(.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) #s(literal 2 binary64))
(.f64 #s(literal 2 binary64) (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (pow.f64 (sin.f64 x) #s(literal 2 binary64))) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))))
(/.f64 (-.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (pow.f64 (sin.f64 x) #s(literal 3 binary64))) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64))))
(fma.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(fma.f64 (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 2 binary64)) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x)))))
(-.f64 (/.f64 (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (sin.f64 x) #s(literal 3 binary64)) (fma.f64 (sin.f64 x) (+.f64 (sin.f64 x) (sin.f64 (+.f64 eps x))) (pow.f64 (sin.f64 (+.f64 eps x)) #s(literal 2 binary64)))))
(-.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x) (sin.f64 x)))
(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps) (sin.f64 x)))
(-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (sin.f64 x)))
(+.f64 (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 (+.f64 (+.f64 eps x) x) #s(literal 2 binary64))) (sin.f64 (/.f64 (-.f64 (+.f64 eps x) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))) (fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))) (fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))) (-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps))))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)))) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)) (fma.f64 (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (*.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)) (fma.f64 (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (*.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x)) (-.f64 (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps))))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) (sin.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (cos.f64 eps) (sin.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)) (-.f64 (.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (sin.f64 x))) (.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (sin.f64 x))))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (cos.f64 x) (sin.f64 eps) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (cos.f64 eps) (sin.f64 x) (*.f64 (cos.f64 x) (sin.f64 eps)))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(fma.f64 (sin.f64 eps) (cos.f64 x) (*.f64 (cos.f64 eps) (sin.f64 x)))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(fma.f64 (sin.f64 x) (cos.f64 eps) (*.f64 (cos.f64 x) (sin.f64 eps)))
(sin.f64 (+.f64 eps x))
(-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (cos.f64 x)) (sin.f64 eps)))
(-.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (sin.f64 eps)) (cos.f64 x)))
(-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (neg.f64 (cos.f64 eps)) (sin.f64 x)))
(-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (neg.f64 (sin.f64 x)) (cos.f64 eps)))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (neg.f64 (cos.f64 x)) (neg.f64 (sin.f64 eps))))
(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (cos.f64 x) (sin.f64 eps)))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (neg.f64 (cos.f64 eps)) (neg.f64 (sin.f64 x))))
(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (cos.f64 eps) (sin.f64 x)))
(/.f64 (neg.f64 (*.f64 (-.f64 x eps) (+.f64 eps x))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (*.f64 (-.f64 eps x) (+.f64 eps x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps (-.f64 eps x) (*.f64 x x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (*.f64 x (-.f64 x eps)))))
(/.f64 (*.f64 (-.f64 x eps) (+.f64 eps x)) (-.f64 x eps))
(/.f64 (*.f64 (-.f64 eps x) (+.f64 eps x)) (-.f64 eps x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps (-.f64 eps x) (*.f64 x x)))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 eps eps (*.f64 x (-.f64 x eps))))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 (neg.f64 eps) #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(-.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 eps (neg.f64 x))
(-.f64 x (neg.f64 eps))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps (-.f64 eps x) (.f64 x x))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (.f64 x (-.f64 x eps)))))
(+.f64 eps (*.f64 (neg.f64 x) #s(literal -1 binary64)))
(+.f64 eps x)
(+.f64 x (*.f64 (neg.f64 eps) #s(literal -1 binary64)))
(+.f64 x eps)
x
eps
(sin.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (-.f64 (cos.f64 eps) #s(literal 1 binary64))) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (sin.f64 eps))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 eps) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 eps) x) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 eps))) x (cos.f64 eps)) x (sin.f64 eps)))
#s(approx (+ x eps) eps)
#s(approx (+ x eps) (+.f64 eps x))
#s(approx x x)
#s(approx (sin x) x)
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/6 binary64) x))
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) x))
#s(approx (sin x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) x)
#s(approx (+ x eps) (fma.f64 (/.f64 eps x) x x))
#s(approx (sin x) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 x) (fma.f64 #s(literal -1 binary64) (/.f64 eps x) #s(literal -1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (sin (+ x eps)) (sin.f64 x))
#s(approx (sin (+ x eps)) (fma.f64 (cos.f64 x) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps (sin.f64 x)))
#s(approx (sin (+ x eps)) (fma.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps (sin.f64 x)))
#s(approx eps eps)
#s(approx (+ x eps) (fma.f64 (/.f64 x eps) eps eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (sin (+ x eps)) (sin.f64 (+.f64 eps x)))
#s(approx (+ x eps) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal -1 binary64) #s(literal -1 binary64))))

eval11.0ms (0.2%)

Memory: 0.7MiB live, 8.3MiB allocated; 1ms collecting garbage
Compiler: Compiled 1 964 to 373 computations (81% saved)

prune3.0ms (0.1%)

Memory

-3.2MiB live, 4.5MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	3	104

Accuracy

100.0%

Counts

104 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Status

Accuracy

Program

▶

100.0%

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))

▶

99.9%

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))

▶

99.3%

#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))

Compiler

Compiled 40 to 30 computations (25% saved)

series12.0ms (0.3%)

Memory

-1.3MiB live, 6.2MiB allocated; 0ms collecting garbage

Counts

13 → 55

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
#s(literal -1/2 binary64)

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#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 x #s(hole binary64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
2.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
2.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
2.0ms	x	@	0	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)
1.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (sin eps) eps (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) x (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) -1/2)

rewrite137.0ms (3.1%)

Memory

-23.2MiB live, 47.2MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	253	989
0	265	978
1	1568	978
0	8144	929

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

68 → 106

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(cos.f64 x)
x
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 (sin.f64 x) eps)
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#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 x #s(hole binary64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (sin eps) #s(hole binary64 eps))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* -1/6 (pow eps 2))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))))
#s(approx (sin eps) #s(hole binary64 (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))))
#s(approx eps #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (sin eps) #s(hole binary64 (sin eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
(sin.f64 eps)
eps
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
(*.f64 (cos.f64 x) eps)
(*.f64 eps (cos.f64 x))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
x
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(.f64 eps (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps)) (.f64 (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))) (-.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))
(/.f64 (-.f64 (.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps)) (.f64 (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))))) (-.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps) (-.f64 (.f64 (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)) (.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps)))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (cos.f64 x) eps) (.f64 (cos.f64 x) eps) (-.f64 (.f64 (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))) (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))) (.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))))
(fma.f64 (cos.f64 x) eps (.f64 (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))))
(fma.f64 eps (cos.f64 x) (.f64 (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) eps))
(+.f64 (.f64 (cos.f64 x) eps) (.f64 eps (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps)) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps)) (.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 (sin.f64 x) eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))))))
(/.f64 (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x)))))
(fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(fma.f64 (*.f64 #s(literal -1/2 binary64) eps) (sin.f64 x) (cos.f64 x))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (sin.f64 x) eps) (cos.f64 x))
(fma.f64 (sin.f64 x) (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x))
(-.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))))
(-.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps)))
(+.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))) (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))))))
(+.f64 (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
(*.f64 (sin.f64 x) eps)
(*.f64 eps (sin.f64 x))
(sin.f64 x)
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (cos.f64 eps) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (fma.f64 (*.f64 (sin.f64 eps) x) #s(literal -1/2 binary64) (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (fma.f64 (-.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (cos.f64 eps) #s(literal 1/6 binary64)) x (*.f64 (sin.f64 eps) #s(literal -1/2 binary64))) x (cos.f64 eps)) #s(literal 1 binary64)) x (sin.f64 eps)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx x x)
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal 1/12 binary64) (.f64 (.f64 eps eps) x) (.f64 #s(literal -1/2 binary64) eps)) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))) x eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 eps x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 (cos.f64 x) #s(literal -1/6 binary64))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (sin eps) eps)
#s(approx (sin eps) (.f64 (fma.f64 (.f64 eps eps) #s(literal -1/6 binary64) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx (sin eps) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 eps eps) #s(literal 1/120 binary64)) (.f64 eps eps)) #s(literal 1/6 binary64)) (*.f64 eps eps) #s(literal 1 binary64)) eps))
#s(approx eps eps)
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx (sin eps) (sin.f64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))

eval13.0ms (0.3%)

Memory: 2.7MiB live, 10.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 3 170 to 507 computations (84% saved)

prune5.0ms (0.1%)

Memory

-1.3MiB live, 6.6MiB allocated; 1ms collecting garbage

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	0	0	0
Picked	3	0	3
Done	0	0	0
Total	122	6	128

Accuracy

100.0%

Counts

128 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
▶	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)))
▶	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
▶	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))

Compiler

Compiled 292 to 192 computations (34.2% saved)

series23.0ms (0.5%)

Memory

3.5MiB live, 13.0MiB allocated; 0ms collecting garbage

Counts

29 → 111

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 #s(approx (sin x) x) eps)
#s(approx (sin x) x)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)
(.f64 (.f64 x x) eps)
(*.f64 x x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
(+.f64 eps x)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)
(.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps)))
(fma.f64 eps x (*.f64 eps eps))
(*.f64 eps eps)

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#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 x #s(hole binary64 x))
#s(approx (cos x) #s(hole binary64 1))
#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 (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 eps))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps x)))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) x eps -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ eps x)) x) 1) (* -1/2 (+ eps x)) (+ eps x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps))
4.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) x eps -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ eps x)) x) 1) (* -1/2 (+ eps x)) (+ eps x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps))
3.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) x eps -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ eps x)) x) 1) (* -1/2 (+ eps x)) (+ eps x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps))
3.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) x eps -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ eps x)) x) 1) (* -1/2 (+ eps x)) (+ eps x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps))
3.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x) x eps -1/2 (cos x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (+ (* (* (* x x) eps) -1/2) eps) (* (* x x) eps) (* x x) (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (+ (* (* -1/2 (+ eps x)) x) 1) (* -1/2 (+ eps x)) (+ eps x) 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (* -1/2 (+ (* eps x) (* eps eps))) (+ (* eps x) (* eps eps)) (* eps eps))

rewrite154.0ms (3.5%)

Memory

6.4MiB live, 54.5MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	416	2241
0	439	2143
1	2330	2143
0	8607	2052

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

140 → 306

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps)
(fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(*.f64 #s(approx (sin x) x) eps)
#s(approx (sin x) x)
x
eps
#s(literal -1/2 binary64)
(cos.f64 x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)
(.f64 (.f64 x x) eps)
(*.f64 x x)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
(+.f64 eps x)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps))
(fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)
(.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps)))
(fma.f64 eps x (*.f64 eps eps))
(*.f64 eps eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#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 x #s(hole binary64 x))
#s(approx (cos x) #s(hole binary64 1))
#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 (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 eps))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (* x x) eps) #s(hole binary64 (* eps (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 1))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1/2 eps)))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (+ (* -1/2 eps) (* -1/2 x))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 eps))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (pow eps 2)))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* -1/2 (pow x 2))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* (pow x 2) (- (+ (* -1/2 (/ eps x)) (/ 1 (pow x 2))) 1/2))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1/2 x)))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* x (- (* -1/2 (/ eps x)) 1/2))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps x)))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* (pow x 2) (- (* -1 (/ (- (* 1/2 eps) (/ 1 x)) x)) 1/2))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1 (* x (+ 1/2 (* 1/2 (/ eps x)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* eps (+ eps x))))
#s(approx (* eps eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* eps (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* eps (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) #s(hole binary64 (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (+ (* eps x) (* eps eps)) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) #s(hole binary64 (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (+ 1 (* -1/2 (pow x 2))) eps)) (* 1/2 x))))))
#s(approx (* -1/2 (+ eps x)) #s(hole binary64 (* -1 (* eps (+ 1/2 (* 1/2 (/ x eps)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps) (cos.f64 x)) eps))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps) (cos.f64 x)) eps)
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps) (cos.f64 x)))
(/.f64 (+.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 3 binary64))) (fma.f64 (cos.f64 x) (cos.f64 x) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 #s(approx (sin x) x) eps))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 #s(approx (sin x) x) eps) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x)))
(/.f64 (fma.f64 (pow.f64 (.f64 #s(approx (sin x) x) eps) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x)))))
(fma.f64 #s(literal -1/2 binary64) (*.f64 #s(approx (sin x) x) eps) (cos.f64 x))
(fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x))
(fma.f64 #s(approx (sin x) x) (*.f64 #s(literal -1/2 binary64) eps) (cos.f64 x))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x))))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x))))))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)) (cos.f64 x))
(+.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 #s(approx (sin x) x) eps)))
(*.f64 #s(approx (sin x) x) eps)
(*.f64 eps #s(approx (sin x) x))
#s(approx (sin x) x)
x
eps
#s(literal -1/2 binary64)
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (fma.f64 #s(literal -1 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 x (/.f64 (PI.f64) #s(literal 2 binary64))))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps)
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 eps (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 eps eps))) (neg.f64 (-.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) eps)))))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 eps (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 eps eps)) (-.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64))))))
(/.f64 (fma.f64 (pow.f64 (.f64 (.f64 x x) eps) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) eps))))
(fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)
(fma.f64 (.f64 x x) (.f64 #s(literal -1/2 binary64) eps) eps)
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 x x) eps)
(fma.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) eps) eps)
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 eps (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) eps)) (/.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) eps)))
(-.f64 eps (.f64 #s(literal 1/2 binary64) (.f64 (*.f64 x x) eps)))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)))))) (/.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) eps)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps)))))
(+.f64 (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)) eps)
(+.f64 eps (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
(.f64 (.f64 x x) eps)
(.f64 eps (.f64 x x))
(.f64 x (.f64 eps x))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps))
(.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))) eps)
(.f64 eps #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (+.f64 eps x) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x)))))
(fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal -1/2 binary64) (*.f64 (+.f64 eps x) x) #s(literal 1 binary64))
(fma.f64 x (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x))) (/.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x))))
(-.f64 #s(literal 1 binary64) (.f64 (neg.f64 x) (.f64 (+.f64 eps x) #s(literal -1/2 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64))))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x))))) (/.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x))))))
(+.f64 (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x))
(*.f64 (+.f64 eps x) #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) (+.f64 eps x))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) eps)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) x))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) x))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) x)))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) x)))))
(fma.f64 #s(literal -1/2 binary64) eps (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal -1/2 binary64) eps))
(fma.f64 eps #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) x))
(fma.f64 x #s(literal -1/2 binary64) (*.f64 #s(literal -1/2 binary64) eps))
(-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) eps) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) x))) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal -1/2 binary64) x))))
(-.f64 (.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/2 binary64) x))
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#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx x x)
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) eps)
#s(approx (+ (* (* (* x x) eps) -1/2) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (* x x) eps) (.f64 (.f64 x x) eps))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) #s(literal 1 binary64))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (fma.f64 (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (* -1/2 (+ eps x)) (*.f64 #s(literal -1/2 binary64) eps))
#s(approx (* -1/2 (+ eps x)) (*.f64 (+.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ eps x) eps)
#s(approx (+ eps x) (+.f64 eps x))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) eps)
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (fma.f64 (.f64 (.f64 eps eps) x) #s(literal -1/2 binary64) eps))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* eps x) (* eps eps)) (*.f64 eps eps))
#s(approx (+ (* eps x) (* eps eps)) (*.f64 (+.f64 eps x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (cos x) (cos.f64 x))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) eps (/.f64 eps (.f64 x x))) (*.f64 x x)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (.f64 (-.f64 (fma.f64 (/.f64 eps x) #s(literal -1/2 binary64) (pow.f64 x #s(literal -2 binary64))) #s(literal 1/2 binary64)) (.f64 x x)))
#s(approx (* -1/2 (+ eps x)) (*.f64 #s(literal -1/2 binary64) x))
#s(approx (* -1/2 (+ eps x)) (.f64 (-.f64 (.f64 (/.f64 eps x) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 eps eps) x) eps)) (.f64 x x)))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 eps eps) x) eps) (/.f64 eps (.f64 x x))) (.f64 x x)))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps)) x))
#s(approx (+ (* eps x) (* eps eps)) (*.f64 eps x))
#s(approx (+ (* eps x) (* eps eps)) (.f64 (+.f64 (/.f64 (.f64 eps eps) x) eps) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (.f64 (-.f64 (neg.f64 (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (pow.f64 x #s(literal -1 binary64))) x)) #s(literal 1/2 binary64)) (*.f64 x x)))
#s(approx (* -1/2 (+ eps x)) (*.f64 (neg.f64 x) (fma.f64 (/.f64 eps x) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 eps eps) (/.f64 (neg.f64 eps) x)) x))) (*.f64 x x)))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (neg.f64 x) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps))))
#s(approx (+ (* eps x) (* eps eps)) (.f64 (neg.f64 x) (.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 (cos.f64 x) eps) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 1/24 binary64) (.f64 (sin.f64 x) eps) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx eps eps)
#s(approx (+ (* (* (* x x) eps) -1/2) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (*.f64 x x)) #s(literal 1 binary64)))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (.f64 (+.f64 eps x) #s(literal -1/2 binary64)) eps))
#s(approx (+ (* eps x) (* eps eps)) (*.f64 (+.f64 eps x) eps))
#s(approx (* eps eps) (*.f64 eps eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (.f64 eps eps)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) eps))
#s(approx (* -1/2 (+ eps x)) (.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) eps))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps eps)))
#s(approx (* -1/2 (+ (* eps x) (* eps eps))) (.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (+ (* eps x) (* eps eps)) (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) (.f64 eps eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))
#s(approx (+ (* (* (* x x) eps) -1/2) eps) (.f64 (neg.f64 eps) (-.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64))))
#s(approx (+ (* (* -1/2 (+ eps x)) x) 1) (.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) x (neg.f64 (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)))))
#s(approx (* -1/2 (+ eps x)) (*.f64 (neg.f64 eps) (fma.f64 (/.f64 x eps) #s(literal 1/2 binary64) #s(literal 1/2 binary64))))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (+ (* (* -1/2 (+ (* eps x) (* eps eps))) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) eps))) (.f64 eps eps)))

eval38.0ms (0.8%)

Memory: -12.5MiB live, 27.2MiB allocated; 3ms collecting garbage
Compiler: Compiled 11 751 to 1 659 computations (85.9% saved)

prune8.0ms (0.2%)

Memory

5.1MiB live, 14.1MiB allocated; 1ms collecting garbage

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	335	2	337
Fresh	0	1	1
Picked	3	2	5
Done	0	0	0
Total	338	5	343

Accuracy

100.0%

Counts

343 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
▶	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
▶	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))

Compiler

Compiled 130 to 85 computations (34.6% saved)

series14.0ms (0.3%)

Memory

1.6MiB live, 9.4MiB allocated; 0ms collecting garbage

Counts

24 → 95

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))
(fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)
(.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64))
(*.f64 (+.f64 eps x) eps)
(+.f64 eps x)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
(.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)
(fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(*.f64 #s(approx (sin x) x) eps)
#s(approx (sin x) x)

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 eps))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ eps x) eps) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#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 (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (* 1/24 (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* eps (+ eps x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (* (* (+ eps x) eps) -1/2) (* (+ eps x) eps) (+ eps x) eps x -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 (* x x) 1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x))
2.0ms	eps	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (* (* (+ eps x) eps) -1/2) (* (+ eps x) eps) (+ eps x) eps x -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 (* x x) 1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x))
2.0ms	x	@	-inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (* (* (+ eps x) eps) -1/2) (* (+ eps x) eps) (+ eps x) eps x -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 (* x x) 1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x))
2.0ms	eps	@	inf	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (* (* (+ eps x) eps) -1/2) (* (+ eps x) eps) (+ eps x) eps x -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 (* x x) 1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x))
2.0ms	eps	@	0	((- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (* (* (+ eps x) eps) -1/2) (* (+ eps x) eps) (+ eps x) eps x -1/2 (- (sin (+ x eps)) (sin x)) (* (cos x) eps) (cos x) (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (- (* 1/24 (* x x)) 1/2) (* 1/24 (* x x)) 1/24 (* x x) 1/2 1 (- (sin (+ x eps)) (sin x)) (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (+ (* (* (sin x) eps) -1/2) (cos x)) (* (sin x) eps) (sin x))

rewrite141.0ms (3.2%)

Memory

-2.1MiB live, 50.7MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	369	1917
0	389	1862
1	2136	1860
0	8049	1785

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

119 → 237

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))
(fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)
(.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64))
(*.f64 (+.f64 eps x) eps)
(+.f64 eps x)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
#s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(.f64 #s(literal 1/24 binary64) (.f64 x x))
#s(literal 1/24 binary64)
(*.f64 x x)
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
(.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps)
(fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
(*.f64 #s(approx (sin x) x) eps)
#s(approx (sin x) x)
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (sin eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (cos eps) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 eps))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (+ eps (* -1/2 (* (pow eps 2) x)))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* -1/2 (pow eps 2))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (pow eps 2)))
#s(approx (* (+ eps x) eps) #s(hole binary64 (+ (* eps x) (pow eps 2))))
#s(approx (+ eps x) #s(hole binary64 eps))
#s(approx (+ eps x) #s(hole binary64 (+ eps x)))
#s(approx x #s(hole binary64 x))
#s(approx (* (cos x) eps) #s(hole binary64 eps))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* -1/2 (* eps (pow x 2))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
#s(approx (* (cos x) eps) #s(hole binary64 (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))))
#s(approx (cos x) #s(hole binary64 1))
#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 (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 1))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 -1/2))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (- (* 1/24 (pow x 2)) 1/2)))
#s(approx (* 1/24 (* x x)) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 1))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* -1/2 (* eps x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* -1/6 (* eps (pow x 2)))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* 1/120 (* eps (pow x 2)))))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* x (+ eps (* (pow x 2) (+ (* -1/6 eps) (* (pow x 2) (+ (* -1/5040 (* eps (pow x 2))) (* 1/120 eps)))))))))
#s(approx (sin x) #s(hole binary64 x))
#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 (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (+ eps x)) (sin x))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* -1/2 (* eps (pow x 2)))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* -1/2 (* eps x))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* eps x)))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* x (+ eps (/ (pow eps 2) x)))))
#s(approx (+ eps x) #s(hole binary64 x))
#s(approx (+ eps x) #s(hole binary64 (* x (+ 1 (/ eps x)))))
#s(approx (* (cos x) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* 1/24 (pow x 4))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(hole binary64 (* (pow x 4) (- (+ 1/24 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* 1/24 (pow x 2))))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(hole binary64 (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (+ (cos x) (* -1/2 (* eps (sin x))))))
#s(approx (* (sin x) eps) #s(hole binary64 (* eps (sin x))))
#s(approx (sin x) #s(hole binary64 (sin x)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- eps (* -1 x))) (sin x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* x (- (* -1 (/ eps x)) 1)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (cos x))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* eps (+ (* -1/6 (cos x)) (* 1/24 (* eps (sin x)))))))))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* eps (cos x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* eps (+ 1 (* -1/2 (pow x 2))))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* eps (+ (* -1/2 eps) (* -1/2 x)))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* eps (+ eps x))))
#s(approx eps #s(hole binary64 eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (cos x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) (sin x)))))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* -1/2 (* (pow eps 2) x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))))
#s(approx (* (* (+ eps x) eps) -1/2) #s(hole binary64 (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))))
#s(approx (* (+ eps x) eps) #s(hole binary64 (* (pow eps 2) (+ 1 (/ x eps)))))
#s(approx (+ eps x) #s(hole binary64 (* eps (+ 1 (/ x eps)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1/2 (* eps (sin x)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))))
#s(approx (- (sin (+ x eps)) (sin x)) #s(hole binary64 (- (sin (- x (* -1 eps))) (sin x))))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) #s(hole binary64 (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))))
#s(approx (+ eps x) #s(hole binary64 (* -1 (* eps (- (* -1 (/ x eps)) 1)))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(hole binary64 (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 eps (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 eps eps))) (neg.f64 (-.f64 (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps)))))
(/.f64 (-.f64 (.f64 eps eps) (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64))) (-.f64 eps (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x)))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 eps eps)) (-.f64 (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps))))
(fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)
(fma.f64 (.f64 (+.f64 eps x) eps) (.f64 #s(literal -1/2 binary64) x) eps)
(fma.f64 x (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) eps)
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x))) (/.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 eps (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps)) (/.f64 (.f64 eps eps) (-.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps)))
(-.f64 eps (.f64 (neg.f64 x) (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64))))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x))))) (/.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (.f64 eps (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x))))))
(+.f64 (/.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 eps eps) (.f64 (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps)))))
(+.f64 (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x) eps)
(+.f64 eps (.f64 (.f64 (*.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x))
(.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64))
(.f64 (+.f64 eps x) (.f64 #s(literal -1/2 binary64) eps))
(.f64 #s(literal -1/2 binary64) (.f64 (+.f64 eps x) eps))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64)) (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps x) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (*.f64 eps x) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps x) #s(literal 3 binary64)) (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))))) (neg.f64 (+.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps x) #s(literal 3 binary64)) (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64)))) (+.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))))
(fma.f64 (.f64 #s(literal -1/2 binary64) eps) x (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps x) #s(literal -1/2 binary64) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) #s(literal -1/2 binary64) (.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 eps x) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))
(fma.f64 #s(literal -1/2 binary64) (.f64 eps eps) (.f64 (*.f64 eps x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (/.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(-.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))) (/.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 eps #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)))))))
(+.f64 (.f64 (.f64 eps eps) #s(literal -1/2 binary64)) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
(+.f64 (.f64 (.f64 eps x) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(*.f64 (+.f64 eps x) eps)
(*.f64 eps (+.f64 eps x))
(/.f64 (+.f64 (pow.f64 eps #s(literal 6 binary64)) (pow.f64 (.f64 eps x) #s(literal 3 binary64))) (+.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (.f64 (.f64 eps eps) (*.f64 eps x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64)))) (neg.f64 (-.f64 (.f64 eps x) (*.f64 eps eps))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 eps x) (*.f64 eps eps))))))
(/.f64 (-.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (pow.f64 eps #s(literal 4 binary64))) (-.f64 (.f64 eps x) (*.f64 eps eps)))
(/.f64 (+.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) (pow.f64 eps #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 eps x) (*.f64 eps eps)))))
(fma.f64 (fabs.f64 (neg.f64 eps)) (fabs.f64 (neg.f64 eps)) (*.f64 eps x))
(fma.f64 (fabs.f64 eps) (fabs.f64 eps) (*.f64 eps x))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (*.f64 eps x))
(fma.f64 (neg.f64 (neg.f64 eps)) (neg.f64 (neg.f64 eps)) (*.f64 eps x))
(fma.f64 (neg.f64 eps) (neg.f64 eps) (*.f64 eps x))
(fma.f64 eps eps (*.f64 eps x))
(fma.f64 eps x (*.f64 eps eps))
(fma.f64 x eps (*.f64 eps eps))
(-.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (-.f64 (.f64 eps x) (.f64 eps eps))) (/.f64 (pow.f64 eps #s(literal 4 binary64)) (-.f64 (.f64 eps x) (*.f64 eps eps))))
(+.f64 (/.f64 (pow.f64 (.f64 eps x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 eps x) (.f64 eps eps))))) (/.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 eps x) #s(literal 2 binary64)) (-.f64 (pow.f64 eps #s(literal 4 binary64)) (.f64 (.f64 eps x) (*.f64 eps eps))))))
(+.f64 (.f64 eps x) (.f64 eps eps))
(+.f64 (.f64 eps eps) (.f64 eps x))
(/.f64 (neg.f64 (-.f64 (.f64 eps eps) (.f64 x x))) (neg.f64 (-.f64 eps x)))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 eps eps))) (neg.f64 (-.f64 x eps)))
(/.f64 (neg.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (.f64 eps eps) (.f64 eps x)))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x x)) (-.f64 eps x))
(/.f64 (-.f64 (.f64 x x) (.f64 eps eps)) (-.f64 x eps))
(/.f64 (+.f64 (pow.f64 eps #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 eps #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 eps eps) (.f64 eps x))))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps x)) (/.f64 (.f64 x x) (-.f64 eps x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x eps)) (/.f64 (.f64 eps eps) (-.f64 x eps)))
(+.f64 (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 eps eps (-.f64 (.f64 x x) (.f64 eps x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (-.f64 (.f64 eps eps) (.f64 eps x)))) (/.f64 (pow.f64 eps #s(literal 3 binary64)) (fma.f64 x x (-.f64 (.f64 eps eps) (.f64 eps x)))))
(+.f64 eps x)
(+.f64 x eps)
eps
x
#s(literal -1/2 binary64)
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
(.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps)
(.f64 eps #s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) x) x) #s(literal 1 binary64))))
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#s(approx (* (cos x) eps) eps)
#s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (.f64 (.f64 x x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (* (cos x) eps) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/24 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/2 binary64) eps)) (.f64 x x) eps))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) #s(literal 1 binary64))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (- (* 1/24 (* x x)) 1/2) #s(literal -1/2 binary64))
#s(approx (- (* 1/24 (* x x)) 1/2) (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
#s(approx (* 1/24 (* x x)) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) #s(literal 1 binary64))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) eps) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/12 binary64) (.f64 eps x)) #s(literal 1/2 binary64)) x (*.f64 #s(literal -1/2 binary64) eps)) x #s(literal 1 binary64)))
#s(approx (* (sin x) eps) (*.f64 eps x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (.f64 (*.f64 x x) eps) #s(literal -1/6 binary64) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (* (sin x) eps) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 (.f64 x x) eps) (.f64 #s(literal 1/120 binary64) eps)) (.f64 x x) (.f64 #s(literal -1/6 binary64) eps)) (*.f64 x x) eps) x))
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 x x) #s(literal -1/6 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (.f64 x x) #s(literal 1/120 binary64)) (.f64 x x)) #s(literal 1/6 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (+.f64 eps x)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (.f64 (*.f64 x x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 eps eps) x) eps)) (.f64 x x)))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (.f64 eps eps) x) eps) (/.f64 eps (.f64 x x))) (.f64 x x)))
#s(approx (* (* (+ eps x) eps) -1/2) (.f64 (.f64 eps x) #s(literal -1/2 binary64)))
#s(approx (* (* (+ eps x) eps) -1/2) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps)) x))
#s(approx (* (+ eps x) eps) (*.f64 eps x))
#s(approx (* (+ eps x) eps) (.f64 (+.f64 (/.f64 (.f64 eps eps) x) eps) x))
#s(approx (+ eps x) x)
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 eps x) #s(literal 1 binary64)) x))
#s(approx (* (cos x) eps) (*.f64 (cos.f64 x) eps))
#s(approx (cos x) (cos.f64 x))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/24 binary64)))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (+ (* (- (* 1/24 (* x x)) 1/2) (* x x)) 1) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal -4 binary64)) #s(literal 1/24 binary64)) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) (pow.f64 x #s(literal 4 binary64))))
#s(approx (- (* 1/24 (* x x)) 1/2) (.f64 (.f64 x x) #s(literal 1/24 binary64)))
#s(approx (- (* 1/24 (* x x)) 1/2) (.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) (*.f64 x x)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)))
#s(approx (* (sin x) eps) (*.f64 (sin.f64 x) eps))
#s(approx (sin x) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 eps (neg.f64 x))) (sin.f64 x)))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) eps (neg.f64 (/.f64 (fma.f64 (.f64 eps eps) #s(literal 1/2 binary64) (/.f64 (neg.f64 eps) x)) x))) (*.f64 x x)))
#s(approx (* (* (+ eps x) eps) -1/2) (.f64 (neg.f64 x) (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps))))
#s(approx (* (+ eps x) eps) (.f64 (neg.f64 x) (.f64 #s(literal -1 binary64) (+.f64 (/.f64 (*.f64 eps eps) x) eps))))
#s(approx (+ eps x) (*.f64 (neg.f64 x) (-.f64 (/.f64 (neg.f64 eps) x) #s(literal 1 binary64))))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (.f64 (cos.f64 x) eps) #s(literal -1/6 binary64) (*.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal 1/24 binary64) (.f64 #s(literal -1/6 binary64) (cos.f64 x))) eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (cos.f64 x)) eps))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (*.f64 (cos.f64 x) eps))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 x x)) #s(literal 1 binary64)) eps))
#s(approx (* (* (+ eps x) eps) -1/2) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) eps))
#s(approx (* (+ eps x) eps) (*.f64 (+.f64 eps x) eps))
#s(approx eps eps)
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (cos.f64 x))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (.f64 (*.f64 eps eps) #s(literal -1/2 binary64)) (sin.f64 x)))
#s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) (.f64 eps eps)))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (.f64 (*.f64 eps eps) x) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)) eps)) (*.f64 eps eps)))
#s(approx (* (* (+ eps x) eps) -1/2) (.f64 (-.f64 (.f64 (/.f64 x eps) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (*.f64 eps eps)))
#s(approx (* (+ eps x) eps) (.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) (.f64 eps eps)))
#s(approx (+ eps x) (*.f64 (+.f64 (/.f64 x eps) #s(literal 1 binary64)) eps))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64)))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) (sin.f64 x) (/.f64 (cos.f64 x) eps)) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (-.f64 (sin.f64 (-.f64 x (neg.f64 eps))) (sin.f64 x)))
#s(approx (+ (* (* (* (+ eps x) eps) -1/2) x) eps) (.f64 (fma.f64 #s(literal -1/2 binary64) x (neg.f64 (/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) eps))) (.f64 eps eps)))
#s(approx (+ eps x) (*.f64 (neg.f64 eps) (-.f64 (/.f64 (neg.f64 x) eps) #s(literal 1 binary64))))
#s(approx (+ (* (* (sin x) eps) -1/2) (cos x)) (*.f64 (neg.f64 eps) (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (neg.f64 (/.f64 (cos.f64 x) eps)))))

eval37.0ms (0.8%)

Memory: 6.7MiB live, 29.2MiB allocated; 2ms collecting garbage
Compiler: Compiled 13 690 to 1 605 computations (88.3% saved)

prune12.0ms (0.3%)

Memory

-3.1MiB live, 16.1MiB allocated; 2ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	359	0	359
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	359	5	364

Accuracy

100.0%

Counts

364 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
✓	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
✓	99.9%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
✓	99.3%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
✓	99.8%	#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))

Compiler

Compiled 386 to 153 computations (60.4% saved)

regimes10.0ms (0.2%)

Memory

-0.8MiB live, 7.1MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (sin.f64 eps))
#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (cos.f64 x) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))
(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 (sin.f64 x) eps) #s(literal -1/2 binary64) (cos.f64 x)) eps))

Outputs

#s(approx (- (sin (+ x eps)) (sin x)) (*.f64 (fma.f64 (*.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (*.f64 #s(literal 1/24 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))

Calls

3 calls:

3.0ms	eps
3.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
100.0%	1	`x`
100.0%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

-2.4MiB live, 5.5MiB allocated; 1ms collecting garbage

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))

Calls

3 calls:

2.0ms	eps
2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes6.0ms (0.1%)

Memory

-3.2MiB live, 5.3MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (+ ( (* (sin x) eps) -1/2) (cos x)) (fma.f64 (*.f64 #s(literal -1/2 binary64) (+.f64 eps x)) x #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 eps x (.f64 eps eps))) x eps)))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))

Calls

3 calls:

2.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.9%	1	`x`
99.9%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes4.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (*.f64 (*.f64 x x) eps) #s(literal -1/2 binary64) eps)))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))

Calls

3 calls:

1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
99.8%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.8%	1	`x`
99.8%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

regimes3.0ms (0.1%)

Memory

-3.5MiB live, 4.4MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

Calls

3 calls:

1.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.0ms	eps
1.0ms	x

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
99.3%	1	`eps`

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify25.0ms (0.6%)

Memory

-1.1MiB live, 6.6MiB allocated; 0ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	130
1	59	130
2	94	130
3	178	130
4	356	130
5	1036	130

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

Outputs
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 (fma.f64 (.f64 #s(approx (sin x) x) eps) #s(literal -1/2 binary64) #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) (.f64 #s(approx (cos x) (fma.f64 (-.f64 (.f64 #s(literal 1/24 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (.f64 x x) #s(literal 1 binary64))) eps))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) (fma.f64 (.f64 (.f64 (+.f64 eps x) eps) #s(literal -1/2 binary64)) x eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (cos x) eps) (fma.f64 (.f64 (.f64 x x) eps) #s(literal -1/2 binary64) eps)))
#s(approx (- (sin (+ x eps)) (sin x)) #s(approx (* (+ (* (* (sin x) eps) -1/2) (cos x)) eps) eps))

derivations168.0ms (3.8%)

Memory

2.5MiB live, 2.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 130 to 41 computations (68.5% saved)

preprocess30.0ms (0.7%)

Memory: 4.1MiB live, 19.9MiB allocated; 2ms collecting garbage
Compiler: Compiled 304 to 120 computations (60.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze28.0ms (0.6%)

sample3.3s (73.2%)

explain86.0ms (1.9%)

preprocess85.0ms (1.9%)

eval0.0ms (0%)

prune0.0ms (0%)

series10.0ms (0.2%)

rewrite128.0ms (2.9%)

eval11.0ms (0.2%)

prune3.0ms (0.1%)

series12.0ms (0.3%)

rewrite137.0ms (3.1%)

eval13.0ms (0.3%)

prune5.0ms (0.1%)

series23.0ms (0.5%)

rewrite154.0ms (3.5%)

eval38.0ms (0.8%)

prune8.0ms (0.2%)

series14.0ms (0.3%)

rewrite141.0ms (3.2%)

eval37.0ms (0.8%)

prune12.0ms (0.3%)

regimes10.0ms (0.2%)

regimes6.0ms (0.1%)

regimes6.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

simplify25.0ms (0.6%)

derivations168.0ms (3.8%)

preprocess30.0ms (0.7%)

end0.0ms (0%)

Profiling