Metrics for 2cos (problem 3.3.5)

analyze44.0ms (0.3%)

Memory

8.6MiB live, 85.8MiB allocated

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)

sample9.9s (58.7%)

Memory

53.8MiB live, 11 566.5MiB allocated

Samples

3.6s	5 648×	2	valid
3.6s	25 882×	0	invalid
668.0ms	2 475×	1	valid
17.0ms	133×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.3s

ival-cos: 3.3s (52.3% of total)

const: 736.0ms (11.6% of total)

adjust: 415.0ms (6.6% of total)

ival-add: 396.0ms (6.3% of total)

ival-sub: 288.0ms (4.6% of total)

ival-fabs: 272.0ms (4.3% of total)

ival-<=: 257.0ms (4.1% of total)

ival-mult: 251.0ms (4% of total)

ival-<: 225.0ms (3.6% of total)

ival-and: 116.0ms (1.8% of total)

exact: 50.0ms (0.8% of total)

ival-assert: 13.0ms (0.2% of total)

Bogosity

preprocess33.0ms (0.2%)

Memory

-4.6MiB live, 34.2MiB allocated

Algorithm

1×	egg-herbie

Rules

108×	`sub-neg`
80×	`lower-fma.f64`
80×	`lower-fma.f32`
80×	`associate--r+`
66×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Stop Event

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

Calls

Call 1

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

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

explain319.0ms (1.9%)

Memory

-30.7MiB live, 294.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
129	1	(1.189698924206829e-160 3.2066630412307237e-164)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
2	0	-	-	`(cos.f64 (+.f64 x eps))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`	cancellation	130	0
`cos.f64`	`(cos.f64 (+.f64 x eps))`	sensitivity	2	0

Confusion

	Predicted +	Predicted -
+	131	0
-	1	124

Precision

0.9924242424242424

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	131	0	0
-	1	0	124

Precision?

0.9924242424242424

Recall?

1.0

Freqs

test

number	freq
0	124
1	132

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

224.0ms	366×	2	valid
28.0ms	136×	1	valid
1.0ms	10×	0	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 228.0ms

ival-cos: 174.0ms (76.2% of total)

adjust: 27.0ms (11.8% of total)

ival-sub: 24.0ms (10.5% of total)

ival-add: 3.0ms (1.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune5.0ms (0%)

Memory

-36.3MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize143.0ms (0.8%)

Memory

28.2MiB live, 100.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	54.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

125.0ms	183×	2	valid
9.0ms	68×	1	valid
0.0ms	5×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 122.0ms

ival-cos: 108.0ms (88.8% of total)

adjust: 9.0ms (7.4% of total)

ival-sub: 3.0ms (2.5% of total)

ival-add: 2.0ms (1.6% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series4.0ms (0%)

Memory

14.5MiB live, 14.5MiB allocated

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))>
#<alt (cos.f64 (+.f64 x eps))>
#<alt (cos.f64 x)>
#<alt (+.f64 x eps)>

Outputs
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (- (cos (- eps (* -1 x))) (cos x))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (+ eps x)) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (- (cos (- x (* -1 eps))) (cos x))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	eps	@	0	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	inf	(+ x eps)

rewrite339.0ms (2%)

Memory

-24.2MiB live, 573.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 936×	`lower-fma.f64`
4 936×	`lower-fma.f32`
4 656×	`lower-*.f64`
4 656×	`lower-*.f32`
2 192×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16

Stop Event

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

Counts

4 → 228

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))) #s(literal -1 binary64)))
(+.f64 (cos.f64 (+.f64 x eps)) (neg.f64 (cos.f64 x)))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(+.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (-.f64 (neg.f64 (.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (+.f64 x eps)))
(+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(+.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (neg.f64 (.f64 (sin.f64 x) (sin.f64 eps))))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(-.f64 (*.f64 (cos.f64 x) (cos.f64 eps)) (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x)))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))))
(-.f64 #s(literal 0 binary64) (-.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))))
(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (+.f64 (cos.f64 (+.f64 x eps)) #s(literal 0 binary64)) (cos.f64 x))
(fma.f64 (cos.f64 (+.f64 x eps)) (/.f64 (cos.f64 (+.f64 x eps)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(fma.f64 (cos.f64 (+.f64 x eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (cos.f64 x) (cos.f64 eps) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(fma.f64 (cos.f64 x) #s(literal -1 binary64) (cos.f64 (+.f64 x eps)))
(fma.f64 (cos.f64 eps) (cos.f64 x) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (cos.f64 eps) (cos.f64 x) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(fma.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (neg.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))))
(fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (/.f64 (cos.f64 (+.f64 x eps)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(fma.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(fma.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (fma.f64 (sin.f64 x) (sin.f64 (neg.f64 eps)) (neg.f64 (cos.f64 x))))
(fma.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64) (-.f64 (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps))) (cos.f64 x)))
(fma.f64 (-.f64 (pow.f64 (.f64 (cos.f64 x) (cos.f64 eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (sin.f64 eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) eps)))) (.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (cos.f64 (-.f64 x eps))))) (neg.f64 (cos.f64 x)))
(fma.f64 #s(literal -1 binary64) (cos.f64 x) (cos.f64 (+.f64 x eps)))
(fma.f64 (*.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) (/.f64 #s(literal 1 binary64) (cos.f64 (-.f64 x eps))) (neg.f64 (cos.f64 x)))
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(.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (/.f64 (+.f64 x eps) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))))
(.f64 (.f64 (+.f64 x eps) (neg.f64 (-.f64 x eps))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 x eps))))
(*.f64 #s(literal 1 binary64) (+.f64 x eps))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps))) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (.f64 eps eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x x) (.f64 eps (*.f64 eps eps)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x eps) (-.f64 x eps))) #s(literal -1 binary64)))
(.f64 (.f64 (+.f64 x eps) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (*.f64 (+.f64 x eps) (-.f64 x eps))) (+.f64 x eps))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps (-.f64 eps x)) (.f64 (.f64 eps (-.f64 eps x)) (.f64 eps (-.f64 eps x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (fma.f64 (.f64 eps (-.f64 eps x)) (-.f64 (.f64 eps (-.f64 eps x)) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))) (-.f64 (.f64 x x) (.f64 eps (-.f64 eps x))))
(.f64 (/.f64 (.f64 (+.f64 x eps) (-.f64 x eps)) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))) (fma.f64 x x (*.f64 eps (+.f64 x eps))))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 x x (.f64 eps eps)) (.f64 x (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (-.f64 x eps) (.f64 (fma.f64 x x (.f64 eps eps)) (.f64 (+.f64 x eps) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 eps eps))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (-.f64 x eps) (.f64 eps eps)) (.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 eps (+.f64 x eps))) (-.f64 x eps))))

simplify435.0ms (2.6%)

Memory

2.0MiB live, 593.1MiB allocated

Algorithm

1×	egg-herbie

Rules

14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
4 148×	`lower-*.f64`
4 148×	`lower-*.f32`
3 720×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	609	495
3	2401	494
4	7937	494
0	8087	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 78

Calls

Call 1

Inputs
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(- (cos (- eps (* -1 x))) (cos x))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (+ eps x)) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(- (cos (- x (* -1 eps))) (cos x))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))

Outputs
(- (cos eps) 1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(-.f64 (cos.f64 eps) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(-.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (.f64 x (*.f64 x #s(literal 1/2 binary64)))) (fma.f64 x (sin.f64 eps) #s(literal 1 binary64)))
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(+.f64 #s(literal -1 binary64) (fma.f64 x (.f64 x #s(literal 1/2 binary64)) (fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (.f64 x (.f64 (sin.f64 eps) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- eps (* -1 x))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (+ eps x)) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(- (cos (- x (* -1 eps))) (cos x))
(-.f64 (cos.f64 (+.f64 eps x)) (cos.f64 x))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(-.f64 (cos.f64 eps) (*.f64 x (sin.f64 eps)))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(fma.f64 x (sin.f64 (neg.f64 eps)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps)))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 eps) (.f64 x (.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos (- eps (* -1 x)))
(cos.f64 (+.f64 eps x))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1 (* eps (sin x))))
(-.f64 (cos.f64 x) (*.f64 eps (sin.f64 x)))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(-.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x)) (*.f64 eps (sin.f64 x)))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (+ eps x))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
(cos (- x (* -1 eps)))
(cos.f64 (+.f64 eps x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
eps
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
x
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
(* x (+ 1 (/ eps x)))
(+.f64 eps x)
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(+.f64 eps x)
x
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
(+ eps x)
(+.f64 eps x)
eps
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
(* eps (+ 1 (/ x eps)))
(+.f64 eps x)
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(+.f64 eps x)

eval37.0ms (0.2%)

Memory: 31.3MiB live, 106.4MiB allocated
Compiler: Compiled 7 945 to 877 computations (89% saved)

prune45.0ms (0.3%)

Memory

2.5MiB live, 123.0MiB allocated

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	292	14	306
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	292	15	307

Accuracy

99.8%

Counts

307 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	54.8%	(fma.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
	54.8%	(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
▶	54.8%	(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
	54.8%	(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
	54.8%	(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) (cos.f64 x))
	54.8%	(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
▶	81.0%	(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
▶	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
▶	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
	99.0%	(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
	98.9%	(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 775 to 348 computations (55.1% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize466.0ms (2.8%)

Memory

7.2MiB live, 1 114.9MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (cos.f64 x) (cos.f64 eps))
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (sin.f64 eps))
✓	accuracy	99.8%	(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	accuracy	55.7%	(+.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
✓	accuracy	100.0%	(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	99.9%	(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
✓	accuracy	54.9%	(-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	55.8%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	accuracy	100.0%	(cos.f64 eps)
✓	accuracy	55.7%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	accuracy	99.8%	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
✓	accuracy	99.6%	(+.f64 x (+.f64 x eps))

Samples

320.0ms	182×	2	valid
70.0ms	69×	1	valid
3.0ms	1×	3	valid
2.0ms	4×	0	valid

Compiler

Compiled 266 to 46 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 343.0ms

ival-cos: 181.0ms (52.7% of total)

adjust: 46.0ms (13.4% of total)

ival-sub: 36.0ms (10.5% of total)

ival-add: 33.0ms (9.6% of total)

ival-mult: 28.0ms (8.2% of total)

ival-sin: 11.0ms (3.2% of total)

ival-div: 4.0ms (1.2% of total)

ival-neg: 3.0ms (0.9% of total)

exact: 1.0ms (0.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series44.0ms (0.3%)

Memory

16.0MiB live, 90.6MiB allocated

Counts

17 → 372

Calls

Call 1

Inputs
#<alt (+.f64 x (+.f64 x eps))>
#<alt (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))>
#<alt (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))>
#<alt (.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))>
#<alt (+.f64 (cos.f64 eps) #s(literal -1 binary64))>
#<alt (cos.f64 eps)>
#<alt (-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))>
#<alt (cos.f64 (+.f64 x eps))>
#<alt (*.f64 x #s(literal -1/2 binary64))>
#<alt (+.f64 x eps)>
#<alt (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))>
#<alt (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))>
#<alt (/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))>
#<alt (+.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps)))>
#<alt (-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))>
#<alt (*.f64 (sin.f64 x) (sin.f64 eps))>
#<alt (*.f64 (cos.f64 x) (cos.f64 eps))>

Outputs
#<alt eps>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* x (+ 2 (/ eps x)))>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 2)))>
#<alt (* 2 x)>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt (+ eps (* 2 x))>
#<alt eps>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt (* eps (+ 1 (* 2 (/ x eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -2 (/ x eps)) 1)))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin (* 1/2 (- eps (* -2 x))))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (+ eps (* 2 x))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (sin (* 1/2 (- (* 2 x) (* -1 eps))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt (- (cos eps) 1)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (cos eps)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))>
#<alt (- (cos x) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))) 1/2)>
#<alt (- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps)))))))) 1/2)>
#<alt (- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))>
#<alt (* -1 (* eps (sin (* 2 x))))>
#<alt (* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))>
#<alt (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))>
#<alt (* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* eps (+ (* 1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x)))))))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))>
#<alt (cos (* 2 eps))>
#<alt (+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))>
#<alt (+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))>
#<alt (+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 (- eps (* -1 x))))>
#<alt (cos (* 2 x))>
#<alt (+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))>
#<alt (+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))>
#<alt (+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (+ eps x)))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (cos (* 2 (- x (* -1 eps))))>
#<alt (/ (- (* 1/2 (cos (* 2 eps))) 1/2) (+ 1 (cos eps)))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (+ (* x (- (* 2/3 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (+ (* 1/6 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))) (/ (* (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))) (- (* -1/2 (cos eps)) 1/2)) (+ 1 (cos eps))))))) (/ 1 (+ 1 (cos eps))))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))>
#<alt (* -1/2 (/ (* eps (sin (* 2 x))) (cos x)))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (+ (* 1/3 (/ (sin (* 2 x)) (cos x))) (* eps (- (* 1/6 (/ (cos (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x)))))) (cos x))) (+ (* -1/4 (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (* -1/24 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ 1/2 (* -1/2 (cos eps))))) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (* 1/24 (cos eps)) 1/24)))))) 1)>
#<alt (- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (+ (* 1/24 (cos eps)) (* (pow x 2) (+ 1/720 (* -1/720 (cos eps))))) 1/24)))))) 1)>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))>
#<alt (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* 1/24 (cos x)) (* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/40320 (* (pow eps 2) (cos x)))))))))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (* (cos eps) (cos x)) (cos x))>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))>
#<alt (* x (sin eps))>
#<alt (* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))>
#<alt (+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))>
#<alt (+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>
#<alt (* (cos eps) (cos x))>

Calls

93 calls:

Time	Variable		Point	Expression
8.0ms	eps	@	inf	(/ (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (cos (+ x eps)) (cos x)))
5.0ms	eps	@	0	(sin (* (+ x (+ x eps)) 1/2))
2.0ms	eps	@	-inf	(- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2))
1.0ms	x	@	0	(/ (- (+ (* 1/2 (cos (* (+ x eps) 2))) 1/2) (+ (* 1/2 (cos (+ x x))) 1/2)) (+ (cos (+ x eps)) (cos x)))
1.0ms	x	@	inf	(- (+ (neg (cos x)) (* (cos x) (cos eps))) (* (sin x) (sin eps)))

rewrite185.0ms (1.1%)

Memory

-19.9MiB live, 334.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 632×	`lower-fma.f32`
1 626×	`lower-fma.f64`
1 316×	`lower-*.f32`
1 302×	`lower-*.f64`
1 114×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	154
0	76	140
1	299	96
0	2738	95

Stop Event

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

Counts

17 → 454

Calls

Call 1

Inputs
(+.f64 x (+.f64 x eps))
(.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))))
(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(cos.f64 eps)
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(cos.f64 (+.f64 x eps))
(*.f64 x #s(literal -1/2 binary64))
(+.f64 x eps)
(-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))
(cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64)))
(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(+.f64 (neg.f64 (cos.f64 x)) (*.f64 (cos.f64 x) (cos.f64 eps)))
(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(*.f64 (sin.f64 x) (sin.f64 eps))
(*.f64 (cos.f64 x) (cos.f64 eps))

Outputs
eps
(+.f64 x (+.f64 x eps))
(+.f64 x (-.f64 eps x))
(+.f64 eps #s(literal 0 binary64))
(+.f64 (+.f64 x eps) x)
(+.f64 (+.f64 x eps) (neg.f64 x))
(+.f64 #s(literal 0 binary64) eps)
(-.f64 eps #s(literal 0 binary64))
(-.f64 eps (/.f64 #s(literal 0 binary64) eps))
(-.f64 (+.f64 x eps) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) eps)) (/.f64 (.f64 (+.f64 x eps) (+.f64 x eps)) (-.f64 #s(literal 0 binary64) eps)))
(fma.f64 (.f64 eps (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (*.f64 eps eps)) #s(literal 0 binary64))
(fma.f64 (*.f64 eps eps) (/.f64 #s(literal 1 binary64) eps) #s(literal 0 binary64))
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) x)
(fma.f64 (fma.f64 x (.f64 x x) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (fma.f64 eps (-.f64 eps x) (.f64 x x))) (neg.f64 x))
(fma.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (/.f64 #s(literal 1 binary64) (fma.f64 (+.f64 x eps) eps (*.f64 x x))) #s(literal 0 binary64))
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) x)
(fma.f64 (*.f64 (+.f64 x eps) (-.f64 x eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)) (neg.f64 x))
(fma.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) eps)) #s(literal 0 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) (.f64 (fma.f64 (+.f64 x eps) eps (*.f64 x x)) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 eps (-.f64 #s(literal 0 binary64) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps eps) (.f64 eps (*.f64 eps eps))))
(/.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 eps eps)))
(/.f64 (.f64 eps (.f64 eps eps)) (*.f64 eps eps))
(/.f64 (*.f64 eps eps) eps)
(/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) eps (*.f64 x x)))
(/.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps) (fma.f64 (+.f64 x eps) (+.f64 x eps) (-.f64 (.f64 x x) (.f64 x (+.f64 x eps)))))
(/.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) eps)) (-.f64 #s(literal 0 binary64) eps))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) (.f64 eps eps) (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps (.f64 eps eps)))) (.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 eps eps)))
(/.f64 (fma.f64 (.f64 (fma.f64 x x #s(literal 0 binary64)) #s(literal 0 binary64)) eps (.f64 (fma.f64 x x #s(literal 0 binary64)) (.f64 eps eps))) (.f64 (fma.f64 x x #s(literal 0 binary64)) eps))
(/.f64 (fma.f64 #s(literal 0 binary64) (.f64 eps eps) (.f64 #s(literal 0 binary64) (.f64 eps (.f64 eps eps)))) (.f64 #s(literal 0 binary64) (.f64 eps eps)))
(/.f64 (+.f64 #s(literal 0 binary64) (.f64 #s(literal 0 binary64) (.f64 eps eps))) #s(literal 0 binary64))
(/.f64 (neg.f64 (.f64 (fma.f64 (+.f64 x eps) eps (.f64 x x)) eps)) (neg.f64 (fma.f64 (+.f64 x eps) eps (*.f64 x x))))
(/.f64 (neg.f64 (*.f64 eps (-.f64 #s(literal 0 binary64) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (neg.f64 (.f64 eps (.f64 eps eps))) (neg.f64 (*.f64 eps eps)))
(/.f64 (-.f64 (.f64 (+.f64 x eps) (.f64 (+.f64 x eps) (+.f64 x eps))) (.f64 x (.f64 x x))) (fma.f64 (+.f64 x eps) (+.f64 x eps) (fma.f64 x x (*.f64 x (+.f64 x eps)))))
(/.f64 (-.f64 (.f64 eps (.f64 eps eps)) #s(literal 0 binary64)) (*.f64 eps eps))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (fma.f64 eps #s(literal 2 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))))
(.f64 (.f64 (+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (-.f64 x eps))) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))) (/.f64 #s(literal 1 binary64) (+.f64 (neg.f64 (cos.f64 x)) (cos.f64 (-.f64 x eps)))))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -2 binary64)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (fma.f64 eps #s(literal 2 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (+.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (fma.f64 (cos.f64 x) (-.f64 (cos.f64 x) (cos.f64 (+.f64 x eps))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (fma.f64 eps #s(literal 2 binary64) #s(literal 0 binary64))) #s(literal 1/2 binary64))))
(.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (fma.f64 eps #s(literal 2 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64))))) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (fma.f64 eps #s(literal 2 binary64) #s(literal 0 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 #s(literal 0 binary64)))))) (-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(-.f64 (/.f64 (cos.f64 (-.f64 x eps)) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 x eps)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps)))))
(/.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64))
(/.f64 (-.f64 (cos.f64 (-.f64 eps x)) (cos.f64 (+.f64 x eps))) #s(literal 2 binary64))
(/.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps)))) #s(literal -2 binary64))
(*.f64 (sin.f64 x) (sin.f64 eps))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 x eps))) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps)))))
(/.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 2 binary64))
(/.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 eps x))) #s(literal 2 binary64))
(/.f64 (neg.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps)))) #s(literal -2 binary64))
(*.f64 (cos.f64 eps) (cos.f64 x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(*.f64 (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 (-.f64 x eps))) #s(literal 1/2 binary64))

simplify332.0ms (2%)

Memory

-4.2MiB live, 802.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 150×	`lower-fma.f64`
8 150×	`lower-fma.f32`
6 676×	`lower-*.f64`
6 676×	`lower-*.f32`
2 534×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	562	4821
1	1780	4616
2	5112	4590
0	8251	4308

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 363

Calls

Call 1

Inputs
eps
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
(* 2 x)
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* x (+ 2 (/ eps x)))
(* 2 x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(* 2 x)
(+ eps (* 2 x))
(+ eps (* 2 x))
(+ eps (* 2 x))
eps
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
(* eps (+ 1 (* 2 (/ x eps))))
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin (* 1/2 (- eps (* -2 x))))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* (pow eps 2) (- (* 1/40320 (pow eps 2)) 1/720)))) 1/2))
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
(- (cos eps) 1)
1
(+ 1 (* -1/2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 1/24 (pow eps 2)) 1/2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/24 (* -1/720 (pow eps 2)))) 1/2)))
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(cos eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (+ eps x)) (pow x 2))) (/ 1 (pow x 2))))
(* 1/2 (pow x 2))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/2 (/ (cos (- eps (* -1 x))) (pow x 2))) (/ 1 (pow x 2))))
(- (cos x) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (+ eps x)) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(- (cos (- x (* -1 eps))) (+ 1 (* -1/2 (pow x 2))))
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (+ (* -1 (* x (sin (* 2 eps)))) (* 1/2 (cos (* 2 eps)))) 1/2)
(- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (* -1 (cos (* 2 eps)))))))) 1/2)
(- (+ (* 1/2 (cos (* 2 eps))) (* x (+ (* -1 (sin (* 2 eps))) (* x (+ 1 (+ (* -1 (cos (* 2 eps))) (* 2/3 (* x (sin (* 2 eps)))))))))) 1/2)
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x)))))
(* -1 (* eps (sin (* 2 x))))
(* eps (+ (* -1 (sin (* 2 x))) (* -1 (* eps (cos (* 2 x))))))
(* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* 2/3 (* eps (sin (* 2 x))))))))
(* eps (+ (* -1 (sin (* 2 x))) (* eps (+ (* -1 (cos (* 2 x))) (* eps (+ (* 1/3 (* eps (cos (* 2 x)))) (* 2/3 (sin (* 2 x)))))))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x))))
(cos (* 2 eps))
(+ (cos (* 2 eps)) (* -2 (* x (sin (* 2 eps)))))
(+ (cos (* 2 eps)) (* x (- (* -2 (* x (cos (* 2 eps)))) (* 2 (sin (* 2 eps))))))
(+ (cos (* 2 eps)) (* x (- (* x (+ (* -2 (cos (* 2 eps))) (* 4/3 (* x (sin (* 2 eps)))))) (* 2 (sin (* 2 eps))))))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 (- eps (* -1 x))))
(cos (* 2 x))
(+ (cos (* 2 x)) (* -2 (* eps (sin (* 2 x)))))
(+ (cos (* 2 x)) (* eps (- (* -2 (* eps (cos (* 2 x)))) (* 2 (sin (* 2 x))))))
(+ (cos (* 2 x)) (* eps (- (* eps (+ (* -2 (cos (* 2 x))) (* 4/3 (* eps (sin (* 2 x)))))) (* 2 (sin (* 2 x))))))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (+ eps x)))
(cos (* 2 (- x (* -1 eps))))
(cos (* 2 (- x (* -1 eps))))
(cos (* 2 (- x (* -1 eps))))
(cos (* 2 (- x (* -1 eps))))
(/ (- (* 1/2 (cos (* 2 eps))) 1/2) (+ 1 (cos eps)))
(- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))
(- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))
(- (+ (* 1/2 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* x (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (+ (* x (- (* 2/3 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (+ (* -1 (/ (cos (* 2 eps)) (+ 1 (cos eps)))) (/ 1 (+ 1 (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (+ (* 1/6 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))) (/ (* (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))) (- (* -1/2 (cos eps)) 1/2)) (+ 1 (cos eps))))))) (/ 1 (+ 1 (cos eps))))) (+ (* -1 (/ (* (sin eps) (- (* -1 (/ (sin (* 2 eps)) (+ 1 (cos eps)))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2))))) (+ 1 (cos eps)))) (/ (* (- (* -1/2 (cos eps)) 1/2) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* -1 (/ (* (sin eps) (- (* 1/2 (cos (* 2 eps))) 1/2)) (pow (+ 1 (cos eps)) 2)))))) (* 1/2 (/ 1 (+ 1 (cos eps)))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(/ (- (* 1/2 (cos (* 2 (- eps (* -1 x))))) (* 1/2 (cos (neg (* -2 x))))) (+ (cos x) (cos (- eps (* -1 x)))))
(* -1/2 (/ (* eps (sin (* 2 x))) (cos x)))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(* eps (+ (* -1/2 (/ (sin (* 2 x)) (cos x))) (* eps (- (+ (* -1/2 (/ (cos (* 2 x)) (cos x))) (* eps (- (+ (* 1/3 (/ (sin (* 2 x)) (cos x))) (* eps (- (* 1/6 (/ (cos (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* 1/3 (/ (sin (* 2 x)) (cos x))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x)))))) (cos x))) (+ (* -1/4 (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (* -1/24 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))) (+ (* -1/2 (/ (* (sin x) (- (* -1/2 (/ (cos (* 2 x)) (cos x))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2))))) (cos x))) (* 1/8 (/ (sin (* 2 x)) (cos x))))))) (* 1/4 (/ (* (sin x) (sin (* 2 x))) (pow (cos x) 2)))))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (+ eps x)))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (+ eps x))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(/ (- (* 1/2 (cos (* 2 (- x (* -1 eps))))) (* 1/2 (cos (* 2 x)))) (+ (cos x) (cos (- x (* -1 eps)))))
(- (cos eps) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (* -1/2 (cos eps))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (* 1/24 (cos eps)) 1/24)))))) 1)
(- (+ (cos eps) (* (pow x 2) (+ 1/2 (+ (* -1/2 (cos eps)) (* (pow x 2) (- (+ (* 1/24 (cos eps)) (* (pow x 2) (+ 1/720 (* -1/720 (cos eps))))) 1/24)))))) 1)
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x)))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x))))))
(* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* 1/24 (cos x)) (* (pow eps 2) (+ (* -1/720 (cos x)) (* 1/40320 (* (pow eps 2) (cos x)))))))))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (* (cos eps) (cos x)) (cos x))
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (* -1/2 (cos eps)))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ 1/2 (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps)))))) (sin eps)))) 1)
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* 1/24 (* eps (cos x))) (* -1/6 (sin x)))))) (sin x)))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(- (* (cos eps) (cos x)) (+ (cos x) (* (sin eps) (sin x))))
(* x (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(cos eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(cos x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))
(* (cos eps) (cos x))

Outputs
eps
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x)))
(* 2 x)
(*.f64 #s(literal 2 binary64) x)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
(+ eps (* 2 x))
(fma.f64 #s(literal 2 binary64) x eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps)
(* 1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal 1/2 binary64) (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 eps (.f64 #s(literal 1/4 binary64) (cos.f64 x)) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (cos.f64 x))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal -1/48 binary64)) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 #s(literal 1/4 binary64) (cos.f64 x))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 x (.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) (.f64 x #s(literal -1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 (pow.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 2 binary64)) #s(literal -1/2 binary64) (.f64 (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/6 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 x x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x)))))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin (* 1/2 eps))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/2 binary64)) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal -1/2 binary64) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 x #s(literal -1/6 binary64)))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 x))) (sin.f64 x))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
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(/.f64 (.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 (*.f64 #s(literal 2 binary64) x))) (cos.f64 x))
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(.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
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(.f64 eps (fma.f64 eps (.f64 eps (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) (sin.f64 x)))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(.f64 eps (fma.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (sin.f64 x) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(cos eps)
(cos.f64 eps)
(+ (cos eps) (* -1/2 (* (pow x 2) (cos eps))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (cos.f64 eps))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* 1/24 (* (pow x 2) (cos eps))))))
(fma.f64 (.f64 x x) (.f64 (cos.f64 eps) (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))) (cos.f64 eps))
(+ (cos eps) (* (pow x 2) (+ (* -1/2 (cos eps)) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (cos eps))) (* 1/24 (cos eps)))))))
(fma.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (cos.f64 eps) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (cos.f64 eps) (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))))))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* (pow eps 2) (cos x))))
(.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* 1/24 (* (pow eps 2) (cos x))))))
(fma.f64 eps (.f64 eps (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)))) (cos.f64 x))
(+ (cos x) (* (pow eps 2) (+ (* -1/2 (cos x)) (* (pow eps 2) (+ (* -1/720 (* (pow eps 2) (cos x))) (* 1/24 (cos x)))))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (.f64 eps eps) (*.f64 eps eps))))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))
(* (cos eps) (cos x))
(*.f64 (cos.f64 x) (cos.f64 eps))

eval115.0ms (0.7%)

Memory: 15.9MiB live, 288.0MiB allocated
Compiler: Compiled 24 577 to 1 898 computations (92.3% saved)

prune194.0ms (1.1%)

Memory

1.0MiB live, 162.9MiB allocated

Pruning

19 alts after pruning (15 fresh and 4 done)

	Pruned	Kept	Total
New	988	13	1 001
Fresh	7	2	9
Picked	2	3	5
Done	0	1	1
Total	997	19	1 016

Accuracy

100.0%

Counts

1 016 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.9%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	81.0%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
	52.5%	(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 eps)))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))))))) (.f64 (sin.f64 x) (sin.f64 eps)))
▶	99.0%	(-.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	53.4%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
▶	53.1%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
✓	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	53.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
✓	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.7%	(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
▶	98.9%	(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
	54.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	52.3%	(.f64 #s(literal 1/2 binary64) (.f64 x x))

Compiler

Compiled 511 to 346 computations (32.3% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize167.0ms (1%)

Memory

2.4MiB live, 204.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (sin.f64 eps))
✓	accuracy	100.0%	(-.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
✓	accuracy	100.0%	(.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(-.f64 (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	99.9%	(cos.f64 (+.f64 x eps))
✓	accuracy	99.7%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(*.f64 eps #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
✓	accuracy	99.8%	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))

Samples

112.0ms	248×	1	exit
2.0ms	8×	0	valid

Compiler

Compiled 150 to 31 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 96.0ms

adjust: 32.0ms (33.2% of total)

ival-cos: 24.0ms (24.9% of total)

ival-mult: 15.0ms (15.6% of total)

ival-sub: 15.0ms (15.6% of total)

ival-sin: 7.0ms (7.3% of total)

ival-add: 3.0ms (3.1% of total)

exact: 1.0ms (1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series35.0ms (0.2%)

Memory

-0.7MiB live, 36.1MiB allocated

Counts

15 → 288

Calls

Call 1

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

Outputs
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/48 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (* 1/2 eps)>
#<alt (- (cos eps) 1)>
#<alt (- (+ (cos eps) (* -1 (* x (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) 1)>
#<alt (- (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos (- eps (* -1 x))) 1)>
#<alt (- (cos x) 1)>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) 1)>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) 1)>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (+ eps x)) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<alt (- (cos (- x (* -1 eps))) 1)>
#<alt (cos eps)>
#<alt (+ (cos eps) (* -1 (* x (sin eps))))>
#<alt (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))>
#<alt (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos (- eps (* -1 x)))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1 (* eps (sin x))))>
#<alt (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))>
#<alt (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (+ eps x))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt (cos (- x (* -1 eps)))>
#<alt eps>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt x>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt (* x (+ 1 (/ eps x)))>
#<alt x>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1 (/ eps x)) 1)))>
#<alt x>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt (+ eps x)>
#<alt eps>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt (* eps (+ 1 (/ x eps)))>
#<alt eps>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1)))>
#<alt (* -1 (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (- (* -1/2 (* eps (cos x))) (sin x))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))>
#<alt (+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1/2 (* eps (cos x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* x (sin eps))) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (- (* 1/4 (* (pow eps 2) x)) (sin eps))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (- (* x (+ (* 1/6 (* x (sin eps))) (* 1/4 (pow eps 2)))) (sin eps))))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (- (* -1/2 (* eps (cos x))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))>
#<alt (* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* -1/120 (* (pow eps 2) (sin x))) (* -1/6 (sin x)))))) (sin x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))>
#<alt (* x (sin eps))>
#<alt (* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))>
#<alt (* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* eps (sin x))>
#<alt (* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))>
#<alt (* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt (* (sin eps) (sin x))>
#<alt eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>

Calls

72 calls:

Time	Variable		Point	Expression
17.0ms	eps	@	inf	(* eps (* (cos x) -1/2))
6.0ms	x	@	inf	(- (* (cos x) (* eps (* eps -1/2))) (* (sin x) (sin eps)))
1.0ms	x	@	inf	(- (* eps (* (cos x) -1/2)) (sin x))
0.0ms	x	@	-inf	(- (* (cos x) (* eps (* eps -1/2))) (* (sin x) (sin eps)))
0.0ms	x	@	-inf	(- (* eps (* (cos x) -1/2)) (sin x))

rewrite606.0ms (3.6%)

Memory

-19.1MiB live, 564.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 618×	`lower-fma.f32`
6 616×	`lower-fma.f64`
4 782×	`lower-*.f32`
4 764×	`lower-*.f64`
3 752×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	85
0	49	85
1	150	85
2	1011	85
0	8380	85

Stop Event

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

Counts

15 → 375

Calls

Call 1

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

Outputs
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))
(-.f64 (.f64 (sin.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (cos.f64 (/.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (.f64 (cos.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (/.f64 (.f64 x x) (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (/.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (cos.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))
(fma.f64 (+.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 1/2 binary64) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))) (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))))
(/.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64)))))))))
(/.f64 (neg.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x)))) (neg.f64 (sin.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64))) (-.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(.f64 (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))))))))
(.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (sin.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) x))))
(+.f64 (.f64 (cos.f64 (neg.f64 x)) #s(literal 1/2 binary64)) (neg.f64 (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 1/2 binary64))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(+.f64 (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(-.f64 (.f64 (cos.f64 (neg.f64 x)) #s(literal 1/2 binary64)) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (cos.f64 (+.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (.f64 eps #s(literal -1/2 binary64)))) #s(literal 2 binary64)) (.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(fma.f64 (cos.f64 (neg.f64 x)) #s(literal 1/2 binary64) (neg.f64 (*.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 1/2 binary64))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (-.f64 (cos.f64 (neg.f64 x)) (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x)))) #s(literal -2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal 1 binary64)))
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(.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (sin.f64 eps)))
(*.f64 (sin.f64 x) (sin.f64 eps))
(*.f64 (sin.f64 eps) (sin.f64 x))
(*.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x))) #s(literal 1/2 binary64))
(*.f64 (neg.f64 (-.f64 (cos.f64 (-.f64 x eps)) (cos.f64 (+.f64 eps x)))) #s(literal -1/2 binary64))
(sin.f64 eps)

simplify392.0ms (2.3%)

Memory

16.9MiB live, 877.0MiB allocated

Algorithm

1×	egg-herbie

Rules

15 010×	`lower-fma.f64`
15 010×	`lower-fma.f32`
5 830×	`lower-*.f64`
5 830×	`lower-*.f32`
3 492×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	324	2432
1	993	2398
2	2610	2363
3	5821	2357
0	8114	2231

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 281

Calls

Call 1

Inputs
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x))))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(sin (* 1/2 eps))
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(* 1/2 eps)
(- (cos eps) 1)
(- (+ (cos eps) (* -1 (* x (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps)))) 1)
(- (+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps)))) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos (- eps (* -1 x))) 1)
(- (cos x) 1)
(- (+ (cos x) (* -1 (* eps (sin x)))) 1)
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) 1)
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (+ eps x)) 1)
(- (cos (- x (* -1 eps))) 1)
(- (cos (- x (* -1 eps))) 1)
(- (cos (- x (* -1 eps))) 1)
(- (cos (- x (* -1 eps))) 1)
(cos eps)
(+ (cos eps) (* -1 (* x (sin eps))))
(+ (cos eps) (* x (- (* -1/2 (* x (cos eps))) (sin eps))))
(+ (cos eps) (* x (- (* x (+ (* -1/2 (cos eps)) (* 1/6 (* x (sin eps))))) (sin eps))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos (- eps (* -1 x)))
(cos x)
(+ (cos x) (* -1 (* eps (sin x))))
(+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x))))
(+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x))))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (+ eps x))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
(cos (- x (* -1 eps)))
eps
(+ eps x)
(+ eps x)
(+ eps x)
x
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
(* x (+ 1 (/ eps x)))
x
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
(* -1 (* x (- (* -1 (/ eps x)) 1)))
x
(+ eps x)
(+ eps x)
(+ eps x)
eps
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
(* eps (+ 1 (/ x eps)))
eps
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (* eps (- (* -1 (/ x eps)) 1)))
(* -1 (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* eps (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1 (* eps (+ (* 1/2 (cos x)) (/ (sin x) eps))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(- (* -1/2 (* eps (cos x))) (sin x))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* 1/4 (* eps (pow x 2))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* -1/48 (* eps (pow x 2))) (* 1/4 eps))))
(+ (* -1/2 eps) (* (pow x 2) (+ (* 1/4 eps) (* (pow x 2) (+ (* -1/48 eps) (* 1/1440 (* eps (pow x 2))))))))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1/2 (* eps (cos x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* -1/2 (pow eps 2))
(+ (* -1 (* x (sin eps))) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (- (* 1/4 (* (pow eps 2) x)) (sin eps))))
(+ (* -1/2 (pow eps 2)) (* x (- (* x (+ (* 1/6 (* x (sin eps))) (* 1/4 (pow eps 2)))) (sin eps))))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(* -1 (* eps (sin x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* -1/120 (* (pow eps 2) (sin x))) (* -1/6 (sin x)))))) (sin x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(* -1/2 (* (pow eps 2) (cos x)))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(* x (sin eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* eps (sin x))
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
(* (sin eps) (sin x))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)

Outputs
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (sin.f64 x) (.f64 eps (*.f64 #s(literal 1/2 binary64) (cos.f64 x))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 (sin.f64 x) (.f64 eps #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 eps (*.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- x (* -1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (+ x (* 1/2 eps)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (- (* 1/2 eps) (* -1 x)))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 (sin.f64 x) #s(literal 1/2 binary64) (.f64 eps (*.f64 (cos.f64 x) #s(literal 1/4 binary64)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (sin.f64 x) #s(literal -1/12 binary64) (.f64 eps (.f64 #s(literal -1/48 binary64) (cos.f64 x)))) (.f64 (cos.f64 x) #s(literal 1/4 binary64))) (*.f64 (sin.f64 x) #s(literal 1/2 binary64))))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps))))
(.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
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(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1 (* x (sin eps))) (* -1/2 (pow eps 2)))
(fma.f64 (neg.f64 x) (sin.f64 eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(+ (* -1/2 (pow eps 2)) (* x (- (* 1/4 (* (pow eps 2) x)) (sin eps))))
(fma.f64 x (-.f64 (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))) (sin.f64 eps)) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(+ (* -1/2 (pow eps 2)) (* x (- (* x (+ (* 1/6 (* x (sin eps))) (* 1/4 (pow eps 2)))) (sin eps))))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (.f64 (sin.f64 eps) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(- (* -1/2 (* (pow eps 2) (cos x))) (* (sin eps) (sin x)))
(-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 (sin.f64 x) eps))
(* eps (- (* -1/2 (* eps (cos x))) (sin x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 (cos.f64 x) #s(literal -1/2 binary64)))))
(* eps (- (* eps (+ (* -1/2 (cos x)) (* eps (- (* -1/120 (* (pow eps 2) (sin x))) (* -1/6 (sin x)))))) (sin x)))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) (fma.f64 (.f64 eps eps) #s(literal -1/120 binary64) #s(literal 1/6 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 (neg.f64 x))))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(fma.f64 (.f64 (sin.f64 x) (sin.f64 (neg.f64 eps))) #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(fma.f64 (.f64 (sin.f64 x) (sin.f64 (neg.f64 eps))) #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(fma.f64 (.f64 (sin.f64 x) (sin.f64 (neg.f64 eps))) #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* -1/2 (* (pow eps 2) (cos x)))
(.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(fma.f64 (.f64 (sin.f64 x) (sin.f64 (neg.f64 eps))) #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(fma.f64 (.f64 (sin.f64 x) (sin.f64 (neg.f64 eps))) #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* (pow eps 2) (+ (* -1 (/ (* (sin eps) (sin x)) (pow eps 2))) (* -1/2 (cos x))))
(fma.f64 (.f64 (sin.f64 x) (sin.f64 (neg.f64 eps))) #s(literal 1 binary64) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(* x (sin eps))
(*.f64 x (sin.f64 eps))
(* x (+ (sin eps) (* -1/6 (* (pow x 2) (sin eps)))))
(.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (*.f64 x (sin.f64 eps)))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* 1/120 (* (pow x 2) (sin eps)))))))
(.f64 x (.f64 (sin.f64 eps) (+.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/120 binary64))))))
(* x (+ (sin eps) (* (pow x 2) (+ (* -1/6 (sin eps)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (sin eps))) (* 1/120 (sin eps))))))))
(.f64 x (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (sin.f64 eps) (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 eps))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* eps (sin x))
(*.f64 (sin.f64 x) eps)
(* eps (+ (sin x) (* -1/6 (* (pow eps 2) (sin x)))))
(.f64 (sin.f64 x) (fma.f64 eps (.f64 #s(literal -1/6 binary64) (*.f64 eps eps)) eps))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* 1/120 (* (pow eps 2) (sin x)))))))
(.f64 eps (.f64 (sin.f64 x) (+.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (.f64 (.f64 eps eps) (.f64 (*.f64 eps eps) #s(literal 1/120 binary64))))))
(* eps (+ (sin x) (* (pow eps 2) (+ (* -1/6 (sin x)) (* (pow eps 2) (+ (* -1/5040 (* (pow eps 2) (sin x))) (* 1/120 (sin x))))))))
(.f64 eps (fma.f64 (.f64 eps eps) (.f64 (.f64 eps (.f64 (sin.f64 x) eps)) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) (.f64 (fma.f64 #s(literal -1/6 binary64) (.f64 eps eps) #s(literal 1 binary64)) (sin.f64 x))))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
(* (sin eps) (sin x))
(*.f64 (sin.f64 x) (sin.f64 eps))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 #s(literal -1/6 binary64) (.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 eps (.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)))) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)

eval81.0ms (0.5%)

Memory: -9.0MiB live, 227.3MiB allocated
Compiler: Compiled 17 206 to 1 543 computations (91% saved)

prune72.0ms (0.4%)

Memory

9.6MiB live, 185.6MiB allocated

Pruning

24 alts after pruning (19 fresh and 5 done)

	Pruned	Kept	Total
New	657	12	669
Fresh	3	7	10
Picked	3	2	5
Done	1	3	4
Total	664	24	688

Accuracy

100.0%

Counts

688 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.9%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	97.6%	(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
	97.2%	(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
	81.0%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 eps)))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))))))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.1%	(-.f64 (cos.f64 x) #s(literal 1 binary64))
✓	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	99.3%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
▶	99.2%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	98.9%	(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
✓	99.6%	(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
✓	99.7%	(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
▶	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
▶	97.5%	(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
✓	98.9%	(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
	98.6%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.2%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	54.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	52.3%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
▶	53.0%	#s(literal 0 binary64)

Compiler

Compiled 679 to 436 computations (35.8% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

localize165.0ms (1%)

Memory

-17.1MiB live, 178.7MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
✓	accuracy	99.9%	(*.f64 eps #s(literal 1/3840 binary64))
✓	accuracy	99.8%	(.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
✓	accuracy	99.8%	(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(*.f64 (sin.f64 x) (neg.f64 eps))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))
✓	accuracy	99.8%	(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
✓	accuracy	99.5%	(fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))
✓	accuracy	100.0%	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
✓	accuracy	100.0%	(fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))

Samples

81.0ms	253×	0	valid
32.0ms	2×	5	exit
5.0ms	1×	3	valid

Compiler

Compiled 267 to 45 computations (83.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 93.0ms

const: 38.0ms (41.1% of total)

ival-mult: 31.0ms (33.5% of total)

ival-add: 8.0ms (8.6% of total)

ival-sin: 8.0ms (8.6% of total)

ival-cos: 4.0ms (4.3% of total)

adjust: 1.0ms (1.1% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series30.0ms (0.2%)

Memory

-6.1MiB live, 29.2MiB allocated

Counts

15 → 324

Calls

Call 1

Inputs
#<alt (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))>
#<alt (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))>
#<alt (.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))>
#<alt (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))>
#<alt (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))>
#<alt (.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))>
#<alt (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))>
#<alt (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))>
#<alt (*.f64 (sin.f64 x) (neg.f64 eps))>
#<alt (neg.f64 eps)>
#<alt (sin.f64 x)>
#<alt (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))>
#<alt (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))>
#<alt (*.f64 eps #s(literal 1/3840 binary64))>
#<alt (.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))>

Outputs
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (pow (sin (* 1/2 eps)) 2)>
#<alt (+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (pow (sin (* 1/2 eps)) 2))>
#<alt (+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))>
#<alt (+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))>
#<alt (* 1/2 (* eps (cos x)))>
#<alt (* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))>
#<alt (* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* (cos x) (sin (* 1/2 eps)))>
#<alt (* 1/4 eps)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/6 x)>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* x (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* 1/6 x)>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (* 1/4 eps)>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* eps (+ 1/4 (* 1/6 (/ x eps))))>
#<alt (* 1/4 eps)>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))>
#<alt (* eps (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))>
#<alt (* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* -1 (* (pow eps 2) (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))>
#<alt (* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))>
#<alt (* 1/6 (* eps (pow x 3)))>
#<alt (* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt (* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))>
#<alt -1>
#<alt (- (* 1/4 (* eps x)) 1)>
#<alt (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)>
#<alt (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 2) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))>
#<alt (* (pow x 2) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))>
#<alt (* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))>
#<alt (- (* 1/6 (pow x 2)) 1)>
#<alt (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)>
#<alt (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)>
#<alt (- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)>
#<alt (* 1/4 (* eps x))>
#<alt (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))>
#<alt (* 1/4 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))>
#<alt (* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))>
#<alt (* x (- (* 1/6 (pow x 2)) 1))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))>
#<alt (* eps (- (* 1/4 (pow x 2)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))>
#<alt (* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))>
#<alt (* -1 (* eps x))>
#<alt (* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (+ (sin x) (* 1/2 (* eps (cos x))))>
#<alt (+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))>
#<alt (+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (- x (* -1/2 eps)))>
#<alt (sin (* 1/2 eps))>
#<alt (+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))>
#<alt (+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (+ x (* 1/2 eps)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (sin (- (* 1/2 eps) (* -1 x)))>
#<alt (* 1/2 (* eps (sin x)))>
#<alt (* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))>
#<alt (* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))>
#<alt (* 1/3840 (* (pow eps 5) (sin (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (sin (+ x (* 1/2 eps))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* (pow eps 5) (+ (* -1/48 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))))))>
#<alt (* 1/3840 (* (pow eps 5) (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/3840 (sin (- x (* -1/2 eps)))) (* 1/48 (/ (sin (- x (* -1/2 eps))) (pow eps 2))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (sin (- x (* -1/2 eps)))) (* 1/48 (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (sin (- x (* -1/2 eps)))) (* 1/48 (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))))>
#<alt (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))>
#<alt (+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* 1/3840 eps)>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))>
#<alt (* -1/1920 (* (pow eps 5) (sin (+ x (* 1/2 eps)))))>
#<alt (* (pow eps 5) (+ (* -1/1920 (sin (+ x (* 1/2 eps)))) (* 1/24 (/ (sin (+ x (* 1/2 eps))) (pow eps 2)))))>
#<alt (* (pow eps 5) (+ (* -1 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/1920 (sin (+ x (* 1/2 eps)))) (* 1/24 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))))))>
#<alt (* (pow eps 5) (+ (* -1 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/1920 (sin (+ x (* 1/2 eps)))) (* 1/24 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))))))>
#<alt (* -1/1920 (* (pow eps 5) (sin (- x (* -1/2 eps)))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin (- x (* -1/2 eps))) (pow eps 2))) (* 1/1920 (sin (- x (* -1/2 eps)))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/1920 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 4))))))>
#<alt (* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/1920 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 4))))))>
#<alt (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))>
#<alt (+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>
#<alt (* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))>

Calls

81 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(* (* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (sin (+ (* eps 1/2) x))) -2)
1.0ms	x	@	inf	(* (sin (* eps 1/2)) (+ (* (sin x) (cos (* eps 1/2))) (* (sin (* eps 1/2)) (cos x))))
1.0ms	x	@	inf	(* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (sin (+ (* eps 1/2) x)))
1.0ms	eps	@	inf	(* (* eps (+ (* (* eps eps) (+ (* eps (* eps 1/3840)) -1/48)) 1/2)) (sin (+ (* eps 1/2) x)))
1.0ms	eps	@	0	(* eps (+ (* x (+ (* x (+ (* x 1/6) (* eps 1/4))) -1)) (* eps -1/2)))

rewrite333.0ms (2%)

Memory

6.5MiB live, 280.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 290×	`lower-fma.f32`
5 276×	`lower-fma.f64`
4 284×	`lower-*.f32`
4 258×	`lower-*.f64`
3 854×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	163
0	68	136
1	247	136
2	1898	136
0	8330	136

Stop Event

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

Counts

15 → 383

Calls

Call 1

Inputs
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x))
(fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64)))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (.f64 eps #s(literal -1/2 binary64)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(neg.f64 eps)
(sin.f64 x)
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(*.f64 eps #s(literal 1/3840 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))

Outputs
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))))
(+.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))))
(-.f64 (/.f64 (cos.f64 (-.f64 (*.f64 eps #s(literal 1/2 binary64)) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (/.f64 (cos.f64 (fma.f64 eps #s(literal 1/2 binary64) (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal 2 binary64)))
(-.f64 (/.f64 (cos.f64 (-.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (/.f64 (cos.f64 (+.f64 (fma.f64 eps #s(literal 1/2 binary64) x) (.f64 eps #s(literal 1/2 binary64)))) #s(literal 2 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) #s(literal 2 binary64)) (-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))))) (/.f64 (pow.f64 (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))) #s(literal 2 binary64)) (-.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64))))))))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (sin.f64 x) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
(fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (.f64 eps #s(literal 1/2 binary64)))))) (cos.f64 x) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 x) (cos.f64 (*.f64 eps #s(literal 1/2 binary64))))))
(fma.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 x)) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (*.f64 eps #s(literal 1/2 binary64))))))))
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(.f64 eps (.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) #s(literal -2 binary64)))
(.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)) (.f64 eps (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))))
(.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 #s(literal -2 binary64) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) eps) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))))
(.f64 (.f64 #s(literal -2 binary64) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))

simplify344.0ms (2%)

Memory

35.5MiB live, 395.2MiB allocated

Algorithm

1×	egg-herbie

Rules

13 028×	`lower-fma.f64`
13 028×	`lower-fma.f32`
7 174×	`lower-*.f64`
7 174×	`lower-*.f32`
3 494×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	470	4787
1	1567	4586
2	5163	4492
0	8294	4098

Stop Event

1×	iter limit
1×	node limit

Counts

324 → 323

Calls

Call 1

Inputs
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(pow (sin (* 1/2 eps)) 2)
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (pow (sin (* 1/2 eps)) 2))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (+ (* 1/3 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* -2 (* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))))
(* 1/2 (* eps (cos x)))
(* eps (+ (* -1/48 (* (pow eps 2) (cos x))) (* 1/2 (cos x))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* 1/3840 (* (pow eps 2) (cos x)))))))
(* eps (+ (* 1/2 (cos x)) (* (pow eps 2) (+ (* -1/48 (cos x)) (* (pow eps 2) (+ (* -1/645120 (* (pow eps 2) (cos x))) (* 1/3840 (cos x))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* -1/2 (* (pow x 2) (sin (* 1/2 eps)))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* 1/24 (* (pow x 2) (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* (pow x 2) (+ (* -1/2 (sin (* 1/2 eps))) (* (pow x 2) (+ (* -1/720 (* (pow x 2) (sin (* 1/2 eps)))) (* 1/24 (sin (* 1/2 eps))))))))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* (cos x) (sin (* 1/2 eps)))
(* 1/4 eps)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/6 x)
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* x (+ 1/6 (* 1/4 (/ eps x))))
(* 1/6 x)
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* x (- (* -1/4 (/ eps x)) 1/6)))
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* 1/4 eps))
(* 1/4 eps)
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* eps (+ 1/4 (* 1/6 (/ x eps))))
(* 1/4 eps)
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* -1 (* eps (- (* -1/6 (/ x eps)) 1/4)))
(* eps (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 2) (- (* 1/4 (pow x 2)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* (pow eps 2) (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* -1 (* (pow eps 2) (+ 1/2 (* -1/4 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* (pow eps 2) (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)))
(* -1/2 (pow eps 2))
(+ (* -1 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* 1/4 (* (pow eps 2) x)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* -1 eps) (* x (+ (* 1/6 (* eps x)) (* 1/4 (pow eps 2)))))))
(* 1/6 (* eps (pow x 3)))
(* (pow x 3) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x)))))
(* (pow x 3) (+ (* -1 (/ eps (pow x 2))) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* 1/6 eps) (* 1/4 (/ (pow eps 2) x))))))
(* 1/6 (* eps (pow x 3)))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ eps (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* -1/6 eps))))
-1
(- (* 1/4 (* eps x)) 1)
(- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)
(- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 2) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))
(* (pow x 2) (+ 1/6 (* -1 (/ (+ (* -1/4 eps) (/ 1 x)) x))))
(- (* 1/6 (pow x 2)) 1)
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(* 1/4 (* eps x))
(* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* eps (- (+ (* 1/6 (/ (pow x 2) eps)) (* 1/4 x)) (/ 1 eps)))
(* 1/4 (* eps x))
(* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))
(* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))
(* -1 (* eps (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x))))
(* -1/2 eps)
(+ (* -1 x) (* -1/2 eps))
(+ (* -1/2 eps) (* x (- (* 1/4 (* eps x)) 1)))
(+ (* -1/2 eps) (* x (- (* x (+ (* 1/6 x) (* 1/4 eps))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (+ 1/6 (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ 1/6 (* 1/4 (/ eps x))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (+ (* -1/2 (/ eps (pow x 3))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (* -1/4 (/ eps x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/4 eps) (/ 1 x)) x)) 1/6)))
(* -1 (* (pow x 3) (- (* -1 (/ (+ (* -1 (/ (+ 1 (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) 1/6)))
(* x (- (* 1/6 (pow x 2)) 1))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (* 1/4 (pow x 2)) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* eps (- (* 1/4 (pow x 2)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* eps (- (+ (* 1/4 (pow x 2)) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) 1/2))
(* -1 (* eps (+ 1/2 (* -1/4 (pow x 2)))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2))))))
(* -1 (* eps x))
(* x (+ (* -1 eps) (* 1/6 (* eps (pow x 2)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* x (+ (* -1 eps) (* (pow x 2) (+ (* 1/6 eps) (* (pow x 2) (+ (* -1/120 eps) (* 1/5040 (* eps (pow x 2)))))))))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 (* eps (sin x)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (- x (* -1/2 eps)))
(sin (* 1/2 eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (+ x (* 1/2 eps)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(sin (- (* 1/2 eps) (* -1 x)))
(* 1/2 (* eps (sin x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(* 1/3840 (* (pow eps 5) (sin (+ x (* 1/2 eps)))))
(* (pow eps 5) (+ (* -1/48 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))) (* 1/3840 (sin (+ x (* 1/2 eps))))))
(* (pow eps 5) (+ (* -1/48 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))))))
(* (pow eps 5) (+ (* -1/48 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))) (+ (* 1/3840 (sin (+ x (* 1/2 eps)))) (* 1/2 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))))))
(* 1/3840 (* (pow eps 5) (sin (- x (* -1/2 eps)))))
(* -1 (* (pow eps 5) (+ (* -1/3840 (sin (- x (* -1/2 eps)))) (* 1/48 (/ (sin (- x (* -1/2 eps))) (pow eps 2))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (sin (- x (* -1/2 eps)))) (* 1/48 (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))))
(* -1 (* (pow eps 5) (+ (* -1/2 (/ (sin (- x (* -1/2 eps))) (pow eps 4))) (+ (* -1/3840 (sin (- x (* -1/2 eps)))) (* 1/48 (/ (sin (- x (* -1/2 eps))) (pow eps 2)))))))
(* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(+ (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1/2 (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))
(+ (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))) (* x (+ (* -1/2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* -1/6 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* 1/3840 eps)
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(* -1/1920 (* (pow eps 5) (sin (+ x (* 1/2 eps)))))
(* (pow eps 5) (+ (* -1/1920 (sin (+ x (* 1/2 eps)))) (* 1/24 (/ (sin (+ x (* 1/2 eps))) (pow eps 2)))))
(* (pow eps 5) (+ (* -1 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/1920 (sin (+ x (* 1/2 eps)))) (* 1/24 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))))))
(* (pow eps 5) (+ (* -1 (/ (sin (+ x (* 1/2 eps))) (pow eps 4))) (+ (* -1/1920 (sin (+ x (* 1/2 eps)))) (* 1/24 (/ (sin (+ x (* 1/2 eps))) (pow eps 2))))))
(* -1/1920 (* (pow eps 5) (sin (- x (* -1/2 eps)))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin (- x (* -1/2 eps))) (pow eps 2))) (* 1/1920 (sin (- x (* -1/2 eps)))))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/1920 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 4))))))
(* -1 (* (pow eps 5) (+ (* -1/24 (/ (sin (- x (* -1/2 eps))) (pow eps 2))) (+ (* 1/1920 (sin (- x (* -1/2 eps)))) (/ (sin (- x (* -1/2 eps))) (pow eps 4))))))
(* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(+ (* -2 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* eps (* x (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))))))
(+ (* -2 (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* -2 (* eps (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48)))))) (* x (+ (* 1/3 (* eps (* x (* (cos (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))) (* eps (* (sin (* 1/2 eps)) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))

Outputs
(* 1/2 (* eps (sin x)))
(.f64 #s(literal 1/2 binary64) (.f64 eps (sin.f64 x)))
(* eps (+ (* 1/4 (* eps (cos x))) (* 1/2 (sin x))))
(.f64 eps (fma.f64 #s(literal 1/2 binary64) (sin.f64 x) (.f64 eps (*.f64 #s(literal 1/4 binary64) (cos.f64 x)))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/12 binary64)) (.f64 #s(literal 1/4 binary64) (cos.f64 x))) (.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* eps (+ (* 1/2 (sin x)) (* eps (+ (* 1/4 (cos x)) (* eps (+ (* -1/16 (sin x)) (+ (* -1/48 (sin x)) (* -1/48 (* eps (cos x))))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 (.f64 eps (cos.f64 x)) #s(literal -1/48 binary64) (.f64 (sin.f64 x) #s(literal -1/12 binary64))) (.f64 #s(literal 1/4 binary64) (cos.f64 x))) (*.f64 #s(literal 1/2 binary64) (sin.f64 x))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(pow (sin (* 1/2 eps)) 2)
(pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))
(+ (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (pow (sin (* 1/2 eps)) 2))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (* x (+ (* -1/2 (* x (pow (sin (* 1/2 eps)) 2))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))))
(+ (* x (+ (* x (+ (* -1/2 (pow (sin (* 1/2 eps)) 2)) (* -1/6 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))))) (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (pow (sin (* 1/2 eps)) 2))
(fma.f64 x (fma.f64 x (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))))) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(* (sin (* 1/2 eps)) (+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)))))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(+ (sin (* 1/2 eps)) (* x (cos (* 1/2 eps))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* -1/2 (* x (sin (* 1/2 eps)))))))
(fma.f64 x (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (sin.f64 (.f64 #s(literal 1/2 binary64) eps))))
(+ (sin (* 1/2 eps)) (* x (+ (cos (* 1/2 eps)) (* x (+ (* -1/2 (sin (* 1/2 eps))) (* -1/6 (* x (cos (* 1/2 eps)))))))))
(fma.f64 x (fma.f64 x (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal -1/2 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)))) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(sin x)
(sin.f64 x)
(+ (sin x) (* 1/2 (* eps (cos x))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x)) (sin.f64 x))
(+ (sin x) (* eps (+ (* -1/8 (* eps (sin x))) (* 1/2 (cos x)))))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/8 binary64)) #s(literal 1 binary64)) (sin.f64 x) (.f64 #s(literal 1/2 binary64) (*.f64 eps (cos.f64 x))))
(+ (sin x) (* eps (+ (* 1/2 (cos x)) (* eps (+ (* -1/8 (sin x)) (* -1/48 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal -1/8 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal -1/48 binary64) (*.f64 eps eps) #s(literal 1/2 binary64)))) (sin.f64 x))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
(fma.f64 (sin.f64 x) (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 (cos.f64 x) (sin.f64 (*.f64 #s(literal 1/2 binary64) eps))))
(+ (* (cos x) (sin (* 1/2 eps))) (* (cos (* 1/2 eps)) (sin x)))
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(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps #s(literal -2 binary64)))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps #s(literal -2 binary64)))
(* -2 (* eps (* (sin (+ x (* 1/2 eps))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps #s(literal -2 binary64)))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps #s(literal -2 binary64)))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps #s(literal -2 binary64)))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps #s(literal -2 binary64)))
(* -2 (* eps (* (sin (- (* 1/2 eps) (* -1 x))) (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))))
(.f64 (.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 1/3840 binary64) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (*.f64 eps #s(literal -2 binary64)))

eval91.0ms (0.5%)

Memory: -2.2MiB live, 145.5MiB allocated
Compiler: Compiled 22 989 to 1 848 computations (92% saved)

prune88.0ms (0.5%)

Memory

9.9MiB live, 176.2MiB allocated

Pruning

37 alts after pruning (29 fresh and 8 done)

	Pruned	Kept	Total
New	701	17	718
Fresh	2	12	14
Picked	0	5	5
Done	2	3	5
Total	705	37	742

Accuracy

100.0%

Counts

742 → 37

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.9%	(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
	97.2%	(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
	81.0%	(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 eps)))
	99.3%	(-.f64 (.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))))))) (.f64 (sin.f64 x) (sin.f64 eps)))
✓	54.8%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	53.1%	(-.f64 (cos.f64 x) #s(literal 1 binary64))
✓	53.1%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
	79.1%	(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
	79.0%	(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
	78.9%	(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
	99.3%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
	99.3%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
✓	99.2%	(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	99.1%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	98.9%	(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
✓	99.8%	(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
✓	99.7%	(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
	54.4%	(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
	78.8%	(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))))
✓	79.9%	(*.f64 (sin.f64 x) (neg.f64 eps))
	79.1%	(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
	97.5%	(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
✓	97.5%	(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
	97.5%	(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
	48.1%	(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
	97.5%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
	98.6%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
	97.2%	(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
	78.9%	(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
	54.4%	(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
	52.9%	(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
	78.7%	(*.f64 eps (neg.f64 x))
	52.3%	(.f64 #s(literal 1/2 binary64) (.f64 x x))
✓	53.0%	#s(literal 0 binary64)

Compiler

Compiled 1 646 to 648 computations (60.6% saved)

regimes42.0ms (0.2%)

Memory

1.6MiB live, 40.0MiB allocated

Counts

57 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 eps)))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 eps)))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))))))) (.f64 (sin.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) (cos.f64 x))
(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(-.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (cos.f64 (+.f64 x eps)) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64))))))

Outputs

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

Calls

3 calls:

14.0ms	eps
14.0ms	x
12.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes46.0ms (0.3%)

Memory

-57.3MiB live, 47.4MiB allocated

Counts

52 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))
(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 eps x))) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64))) (sin.f64 (.f64 (fma.f64 eps (*.f64 #s(literal 2 binary64) (/.f64 x eps)) eps) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
(-.f64 (.f64 (cos.f64 x) (.f64 eps (.f64 eps #s(literal -1/2 binary64)))) (.f64 (sin.f64 x) (sin.f64 eps)))
(.f64 eps (fma.f64 eps (fma.f64 (cos.f64 x) (+.f64 #s(literal -1/2 binary64) (.f64 eps (.f64 eps #s(literal 1/24 binary64)))) (.f64 eps (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))) (sin.f64 (neg.f64 x))))
(fma.f64 (sin.f64 x) (neg.f64 (sin.f64 eps)) (*.f64 (cos.f64 x) (+.f64 (cos.f64 eps) #s(literal -1 binary64))))
(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 (+.f64 x eps) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (+.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x)))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) (.f64 (cos.f64 x) #s(literal -1/2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 eps)))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (sin.f64 (+.f64 x (.f64 eps #s(literal -1/2 binary64))))) #s(literal 1/2 binary64) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 (cos.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (.f64 (cos.f64 x) (fma.f64 (.f64 eps eps) #s(literal 1/40320 binary64) #s(literal -1/720 binary64))))))) (.f64 (sin.f64 x) (sin.f64 eps)))
(fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (fma.f64 (sin.f64 x) (sin.f64 eps) (cos.f64 x))))
(-.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 eps)) (cos.f64 x)) (.f64 (sin.f64 x) (sin.f64 eps)))
(-.f64 (fma.f64 (cos.f64 x) (cos.f64 eps) (neg.f64 (*.f64 (sin.f64 x) (sin.f64 eps)))) (cos.f64 x))
(-.f64 (+.f64 (neg.f64 (cos.f64 x)) (.f64 (cos.f64 x) (cos.f64 eps))) (.f64 (sin.f64 x) (sin.f64 eps)))

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

Calls

3 calls:

18.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
13.0ms	x
13.0ms	eps

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`eps`
99.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes27.0ms (0.2%)

Memory

16.0MiB live, 16.0MiB allocated

Counts

36 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(.f64 eps (-.f64 (.f64 eps (*.f64 (cos.f64 x) #s(literal -1/2 binary64))) (sin.f64 x)))

Outputs

(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))

Calls

3 calls:

9.0ms	x
9.0ms	eps
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

32 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))

Outputs

(*.f64 (*.f64 (*.f64 eps (fma.f64 (*.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))

Calls

3 calls:

9.0ms	x
8.0ms	eps
7.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`eps`
99.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes25.0ms (0.1%)

Memory

-26.3MiB live, 13.0MiB allocated

Counts

31 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (.f64 eps eps)))))

Outputs
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))

Calls

3 calls:

9.0ms	eps
8.0ms	x
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`eps`
99.1%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes23.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

29 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))

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

Calls

3 calls:

8.0ms	x
8.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`eps`
98.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

28 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(-.f64 (-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64)) (.f64 x (.f64 x #s(literal -1/2 binary64))))

Outputs
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))

Calls

3 calls:

7.0ms	x
7.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.6%	1	`x`
98.6%	1	`eps`
98.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes62.0ms (0.4%)

Memory

-28.1MiB live, 11.4MiB allocated

Counts

25 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) x) (neg.f64 eps))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal 1/5040 binary64) #s(literal -1/120 binary64))) (.f64 eps #s(literal 1/6 binary64))) (neg.f64 eps)))
(.f64 eps (fma.f64 x (.f64 (.f64 x x) (-.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 eps #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) x)) x))) (.f64 eps #s(literal -1/2 binary64))))
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(-.f64 (cos.f64 x) #s(literal 1 binary64))
(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
(*.f64 (sin.f64 x) (neg.f64 eps))

Outputs
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))

Calls

3 calls:

49.0ms	x
7.0ms	eps
6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`eps`
97.6%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

8.5MiB live, 8.5MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))

Outputs
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))

Calls

3 calls:

5.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.5%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 (fma.f64 (.f64 x x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) x) x) (neg.f64 eps))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64))) (neg.f64 eps)) (.f64 eps (.f64 eps #s(literal -1/2 binary64))))

Outputs
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))

Calls

3 calls:

5.0ms	x
5.0ms	eps
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.5%	1	`x`
97.5%	1	`eps`
97.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))

Outputs
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))

Calls

3 calls:

4.0ms	x
4.0ms	eps
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
97.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
97.5%	1	`x`
97.5%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes10.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated

Counts

10 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(.f64 eps (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x x))))
(.f64 eps (.f64 x (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(.f64 (.f64 eps eps) (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps x))

Outputs
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
97.2%	1	`x`
97.2%	1	`eps`
97.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

5 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
(*.f64 eps (neg.f64 x))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(.f64 eps (.f64 eps #s(literal -1/2 binary64)))

Outputs
(*.f64 eps (neg.f64 x))

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
78.7%	1	`x`
78.7%	1	`eps`
78.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes30.0ms (0.2%)

Memory

-36.8MiB live, 4.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))

Outputs
#s(literal 0 binary64)

Calls

3 calls:

27.0ms	x
1.0ms	eps
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
53.0%	1	`eps`
53.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
53.0%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify9.0ms (0.1%)

Memory

5.3MiB live, 5.3MiB allocated

Algorithm

1×	egg-herbie

Rules

74×	`*-commutative_binary64`
12×	`+-commutative_binary64`
12×	`sub-neg_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	74	192
1	116	192
2	128	192
3	135	192
4	137	192

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (neg.f64 x))
#s(literal 0 binary64)

Outputs
(.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (fma.f64 (sin.f64 x) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (cos.f64 x)))) #s(literal -2 binary64))
(.f64 (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (*.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/645120 binary64)) #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))))
(.f64 (.f64 (*.f64 #s(literal 1/2 binary64) eps) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))) #s(literal -2 binary64))
(.f64 #s(literal -2 binary64) (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) (sin.f64 x)))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
(fma.f64 x (fma.f64 x (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (.f64 eps #s(literal 1/4 binary64)))) (neg.f64 eps)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (+.f64 (neg.f64 x) (.f64 eps #s(literal -1/2 binary64)))))
(.f64 eps (fma.f64 (fma.f64 eps #s(literal 1/4 binary64) (.f64 x #s(literal 1/6 binary64))) (.f64 x x) (-.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1 binary64)))))
(.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 eps #s(literal -1/2 binary64))))
(.f64 eps (-.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(*.f64 eps (neg.f64 x))
#s(literal 0 binary64)

soundness1.4s (8.2%)

Memory

29.1MiB live, 425.8MiB allocated

Rules

15 010×	`lower-fma.f64`
15 010×	`lower-fma.f32`
14 158×	`lower-fma.f64`
14 158×	`lower-fma.f32`
13 028×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	16
1	54	16
2	380	16
3	4694	16
0	8209	16
0	470	4787
1	1567	4586
2	5163	4492
0	8294	4098
0	27	85
0	49	85
1	150	85
2	1011	85
0	8380	85
0	562	4821
1	1780	4616
2	5112	4590
0	8251	4308
0	105	498
1	277	495
2	609	495
3	2401	494
4	7937	494
0	8087	474
0	36	163
0	68	136
1	247	136
2	1898	136
0	8330	136
0	324	2432
1	993	2398
2	2610	2363
3	5821	2357
0	8114	2231

Stop Event

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

Compiler

Compiled 675 to 401 computations (40.6% saved)

preprocess104.0ms (0.6%)

Memory: 2.1MiB live, 160.6MiB allocated
Compiler: Compiled 474 to 206 computations (56.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7

analyze44.0ms (0.3%)

sample9.9s (58.7%)

preprocess33.0ms (0.2%)

explain319.0ms (1.9%)

eval0.0ms (0%)

prune5.0ms (0%)

simplify0.0ms (0%)

localize143.0ms (0.8%)

series4.0ms (0%)

rewrite339.0ms (2%)

simplify435.0ms (2.6%)

eval37.0ms (0.2%)

prune45.0ms (0.3%)

simplify0.0ms (0%)

localize466.0ms (2.8%)

series44.0ms (0.3%)

rewrite185.0ms (1.1%)

simplify332.0ms (2%)

eval115.0ms (0.7%)

prune194.0ms (1.1%)

simplify0.0ms (0%)

localize167.0ms (1%)

series35.0ms (0.2%)

rewrite606.0ms (3.6%)

simplify392.0ms (2.3%)

eval81.0ms (0.5%)

prune72.0ms (0.4%)

simplify0.0ms (0%)

localize165.0ms (1%)

series30.0ms (0.2%)

rewrite333.0ms (2%)

simplify344.0ms (2%)

eval91.0ms (0.5%)

prune88.0ms (0.5%)

regimes42.0ms (0.2%)

regimes46.0ms (0.3%)

regimes27.0ms (0.2%)

regimes25.0ms (0.1%)

regimes25.0ms (0.1%)

regimes23.0ms (0.1%)

regimes22.0ms (0.1%)

regimes62.0ms (0.4%)

regimes14.0ms (0.1%)

regimes14.0ms (0.1%)

regimes10.0ms (0.1%)

regimes10.0ms (0.1%)

regimes6.0ms (0%)

regimes30.0ms (0.2%)

simplify9.0ms (0.1%)

soundness1.4s (8.2%)

preprocess104.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	41
1	38	37
2	81	35
3	152	35
4	278	35
5	370	35
6	448	35
7	485	35
8	531	35
9	546	35
10	554	35
0	6	7
0	10	7
1	13	7
2	18	7
3	24	7
4	32	7
5	47	7
6	80	7
7	107	7
8	151	7
9	166	7
10	174	7
0	174	7