Metrics for 2cos (problem 3.3.5)

analyze46.0ms (0.2%)

Memory

-15.1MiB live, 106.9MiB 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)

sample9.5s (51.7%)

Memory

29.8MiB live, 11 974.2MiB allocated

Samples

4.2s	25 979×	0	invalid
2.8s	5 434×	2	valid
776.0ms	2 530×	1	valid
131.0ms	154×	3	valid
16.0ms	138×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 6.1s

ival-cos: 2.6s (42.8% of total)

const: 813.0ms (13.4% of total)

ival-add: 598.0ms (9.9% of total)

ival-<=: 492.0ms (8.1% of total)

ival-sub: 372.0ms (6.1% of total)

ival-fabs: 280.0ms (4.6% of total)

ival-mult: 278.0ms (4.6% of total)

ival-<: 242.0ms (4% of total)

adjust: 228.0ms (3.8% of total)

ival-and: 110.0ms (1.8% of total)

exact: 48.0ms (0.8% of total)

ival-assert: 14.0ms (0.2% of total)

Bogosity

preprocess29.0ms (0.2%)

Memory

32.6MiB live, 68.6MiB allocated

Algorithm

2×	egg-herbie

Rules

116×	`sub-neg`
80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
76×	`associate--r+`
72×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	43	44
2	87	42
3	160	42
4	287	42
5	387	42
6	478	42
7	543	42
8	556	42
9	566	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

Inputs
(- (cos (+ x eps)) (cos x))
(- (cos (+ (neg x) eps)) (cos (neg x)))
(- (cos (+ x (neg eps))) (cos x))
(neg (- (cos (+ (neg x) eps)) (cos (neg x))))
(neg (- (cos (+ x (neg eps))) (cos x)))
(- (cos (+ eps x)) (cos eps))

Outputs
(- (cos (+ x eps)) (cos x))
(- (cos (+ (neg x) eps)) (cos (neg x)))
(- (cos (- eps x)) (cos x))
(- (cos (+ x (neg eps))) (cos x))
(- (cos (- eps x)) (cos x))
(neg (- (cos (+ (neg x) eps)) (cos (neg x))))
(- (cos x) (cos (- eps x)))
(neg (- (cos (+ x (neg eps))) (cos x)))
(- (cos x) (cos (- eps x)))
(- (cos (+ eps x)) (cos eps))
(- (cos (+ x eps)) (cos eps))

explain224.0ms (1.2%)

Memory

-49.6MiB live, 368.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
132	1	(1.6717171481340383e-158 5.123571456757858e-166)	-	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
0	0	-	-	`eps`
0	0	-	-	`(+.f64 x eps)`
0	0	-	-	`(cos.f64 x)`
0	0	-	-	`(cos.f64 (+.f64 x eps))`
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	133	0

Confusion

	Predicted +	Predicted -
+	132	0
-	1	123

Precision

0.9924812030075187

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	132	0	0
-	1	0	123

Precision?

0.9924812030075187

Recall?

1.0

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

129.0ms	348×	2	valid
20.0ms	142×	1	valid
14.0ms	16×	3	valid
0.0ms	6×	0	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 135.0ms

ival-cos: 107.0ms (79.1% of total)

adjust: 17.0ms (12.6% of total)

ival-sub: 6.0ms (4.4% of total)

ival-add: 5.0ms (3.7% of total)

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

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0%)

Memory

15.3MiB live, 15.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(+.f64 x eps)
✓	cost-diff	(cos.f64 (+.f64 x eps))
✓	cost-diff	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Rules

80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
48×	`-lowering-.f32`
48×	`-lowering-.f64`
36×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize105.0ms (0.6%)

Memory

-1.6MiB live, 115.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(cos.f64 (+.f64 x eps))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	52.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Samples

81.0ms	174×	2	valid
9.0ms	71×	1	valid
4.0ms	8×	3	valid
0.0ms	3×	0	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 83.0ms

ival-cos: 47.0ms (56.4% of total)

adjust: 30.0ms (36% of total)

ival-sub: 3.0ms (3.6% of total)

ival-add: 2.0ms (2.4% of total)

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

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

series4.0ms (0%)

Memory

5.7MiB live, 5.7MiB allocated

Counts

4 → 84

Calls

Call 1

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

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 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>
#<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)>

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	eps	@	-inf	(- (cos (+ x eps)) (cos x))
0.0ms	x	@	-inf	(- (cos (+ x eps)) (cos x))

rewrite299.0ms (1.6%)

Memory

0.3MiB live, 427.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 936×	`accelerator-lowering-fma.f32`
4 936×	`accelerator-lowering-fma.f64`
4 656×	`-lowering-.f32`
4 656×	`-lowering-.f64`
2 192×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	50	16
2	376	16
3	4688	16
0	8201	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 228

Calls

Call 1

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

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

simplify389.0ms (2.1%)

Memory

-31.7MiB live, 474.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 158×	`accelerator-lowering-fma.f32`
14 158×	`accelerator-lowering-fma.f64`
4 148×	`-lowering-.f32`
4 148×	`-lowering-.f64`
3 720×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

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)))
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
(+ 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)

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

eval55.0ms (0.3%)

Memory: 3.7MiB live, 79.6MiB allocated
Compiler: Compiled 7 975 to 879 computations (89% saved)

prune48.0ms (0.3%)

Memory

32.9MiB live, 71.4MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	304	8	312
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	304	9	313

Accuracy

99.9%

Counts

313 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.3%	(-.f64 (cos.f64 (+.f64 x eps)) (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)))
	52.2%	(-.f64 (cos.f64 (+.f64 x eps)) (fma.f64 x (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
✓	52.9%	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
	51.9%	(-.f64 (cos.f64 (+.f64 x eps)) #s(literal 1 binary64))
▶	51.9%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
▶	99.7%	(.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))
▶	81.0%	(*.f64 (sin.f64 x) (neg.f64 eps))
▶	99.6%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	99.5%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 235 to 162 computations (31.1% saved)

simplify375.0ms (2.1%)

Memory

-1.8MiB live, 549.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
✓	cost-diff	0	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	cost-diff	0	(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))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(cos.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (cos.f64 (+.f64 x eps)) (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)))
✓	cost-diff	0	(neg.f64 eps)
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(*.f64 (sin.f64 x) (neg.f64 eps))
✓	cost-diff	0	(cos.f64 eps)
✓	cost-diff	0	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	cost-diff	0	(.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))))
✓	cost-diff	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))
✓	cost-diff	192	(+.f64 eps #s(literal 0 binary64))
✓	cost-diff	320	(*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64))

Rules

13 150×	`accelerator-lowering-fma.f32`
13 150×	`accelerator-lowering-fma.f64`
4 466×	`-lowering-.f32`
4 466×	`-lowering-.f64`
1 976×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	234
1	115	234
2	395	232
3	1025	224
4	2267	224
5	4060	224
6	5354	224
7	6715	224
8	7284	224
9	7588	224
10	7835	224
11	7975	224
0	8006	206

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
(* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
(sin (* (+ eps 0) 1/2))
(* (+ eps 0) 1/2)
(+ eps 0)
eps
0
1/2
(sin (* (+ x (+ x eps)) 1/2))
(* (+ x (+ x eps)) 1/2)
(+ x (+ x eps))
x
(+ x eps)
-2
(+ (cos eps) -1)
(cos eps)
eps
-1
(* (sin x) (neg eps))
(sin x)
x
(neg eps)
eps
(- (cos (+ x eps)) (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1))
(cos (+ x eps))
(+ x eps)
x
eps
(+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1)
(* x x)
(+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)
(+ (* x (* x -1/720)) 1/24)
(* x -1/720)
-1/720
1/24
-1/2
1
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
eps
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(* -1/2 (cos x))
-1/2
(cos x)
x
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
(+ (* eps (* eps 1/6)) -1)
(* eps 1/6)
1/6
-1

Outputs
(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (*.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) #s(literal -2 binary64)))
(* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
(.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)))
(sin (* (+ eps 0) 1/2))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(* (+ eps 0) 1/2)
(*.f64 eps #s(literal 1/2 binary64))
(+ eps 0)
eps
eps
0
#s(literal 0 binary64)
1/2
#s(literal 1/2 binary64)
(sin (* (+ x (+ x eps)) 1/2))
(sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x))
(* (+ x (+ x eps)) 1/2)
(fma.f64 eps #s(literal 1/2 binary64) x)
(+ x (+ x eps))
(+.f64 eps (+.f64 x x))
x
(+ x eps)
(+.f64 eps x)
-2
#s(literal -2 binary64)
(+ (cos eps) -1)
(+.f64 (cos.f64 eps) #s(literal -1 binary64))
(cos eps)
(cos.f64 eps)
eps
-1
#s(literal -1 binary64)
(* (sin x) (neg eps))
(neg.f64 (*.f64 eps (sin.f64 x)))
(sin x)
(sin.f64 x)
x
(neg eps)
(neg.f64 eps)
eps
(- (cos (+ x eps)) (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1))
(+.f64 #s(literal -1 binary64) (fma.f64 x (.f64 x (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/720 binary64) #s(literal -1/24 binary64))) #s(literal 1/2 binary64))) (cos.f64 (+.f64 eps x))))
(cos (+ x eps))
(cos.f64 (+.f64 eps x))
(+ x eps)
(+.f64 eps x)
x
eps
(+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1)
(fma.f64 x (.f64 x (fma.f64 x (.f64 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))
(* x x)
(*.f64 x x)
(+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)
(fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))
(+ (* x (* x -1/720)) 1/24)
(fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
(* x -1/720)
(*.f64 x #s(literal -1/720 binary64))
-1/720
#s(literal -1/720 binary64)
1/24
#s(literal 1/24 binary64)
-1/2
#s(literal -1/2 binary64)
1
#s(literal 1 binary64)
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (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))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
x
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(sin x)
(sin.f64 x)
(+ (* eps (* eps 1/6)) -1)
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)

localize384.0ms (2.1%)

Memory

0.6MiB live, 524.9MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	accuracy	99.9%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	accuracy	99.7%	(*.f64 eps #s(literal 1/6 binary64))
✓	accuracy	100.0%	(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))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(*.f64 x #s(literal -1/720 binary64))
✓	accuracy	74.9%	(-.f64 (cos.f64 (+.f64 x eps)) (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)))
✓	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%	(cos.f64 eps)
✓	accuracy	74.4%	(+.f64 (cos.f64 eps) #s(literal -1 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 (+.f64 eps #s(literal 0 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(.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	99.8%	(+.f64 x (+.f64 x eps))

Samples

224.0ms	140×	5	exit
53.0ms	49×	4	valid
30.0ms	45×	2	valid
9.0ms	18×	1	valid
3.0ms	2×	3	valid
1.0ms	2×	0	valid

Compiler

Compiled 231 to 46 computations (80.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 254.0ms

ival-cos: 77.0ms (30.3% of total)

ival-mult: 68.0ms (26.8% of total)

adjust: 50.0ms (19.7% of total)

ival-add: 25.0ms (9.8% of total)

ival-sin: 15.0ms (5.9% of total)

const: 13.0ms (5.1% of total)

ival-sub: 3.0ms (1.2% of total)

exact: 2.0ms (0.8% of total)

ival-neg: 1.0ms (0.4% of total)

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

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

series34.0ms (0.2%)

Memory

-15.7MiB live, 58.7MiB allocated

Counts

23 → 408

Calls

Call 1

Inputs
#<alt (* (+ x (+ x eps)) 1/2)>
#<alt (+ eps 0)>
#<alt (* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)>
#<alt (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))>
#<alt (+ (cos eps) -1)>
#<alt (cos eps)>
#<alt (* (sin x) (neg eps))>
#<alt (sin x)>
#<alt (neg eps)>
#<alt (- (cos (+ x eps)) (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1))>
#<alt (cos (+ x eps))>
#<alt (+ x eps)>
#<alt (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1)>
#<alt (* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))>
#<alt (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))>
#<alt (* -1/2 (cos x))>
#<alt (cos x)>
#<alt (+ x (+ x eps))>
#<alt (sin (* (+ x (+ x eps)) 1/2))>
#<alt (sin (* (+ eps 0) 1/2))>
#<alt (* x -1/720)>
#<alt (+ (* x (* x -1/720)) 1/24)>
#<alt (* eps 1/6)>

Outputs
#<alt (* 1/2 eps)>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt (* x (+ 1 (* 1/2 (/ eps x))))>
#<alt x>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt (* -1 (* x (- (* -1/2 (/ eps x)) 1)))>
#<alt x>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (+ x (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* eps (+ 1/2 (/ x eps)))>
#<alt (* 1/2 eps)>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) 1/2)))>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt eps>
#<alt 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 (* 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 (* -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 (* -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 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 (* -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 (- (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 (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (+ eps x)) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (* 1/720 (pow x 6))>
#<alt (* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (- eps (* -1 x))) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))>
#<alt (- (cos x) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<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 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>
#<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 (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1/720 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)>
#<alt (- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos x))>
#<alt (* -1/2 (cos 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 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 (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 (* 1/2 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 (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt (* -1/720 x)>
#<alt 1/24>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (+ 1/24 (* -1/720 (pow x 2)))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* -1/720 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>

Calls

102 calls:

Time	Variable		Point	Expression
5.0ms	x	@	0	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
3.0ms	eps	@	inf	(- (cos (+ x eps)) (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1))
2.0ms	x	@	-inf	(+ (* x (* x -1/720)) 1/24)
1.0ms	x	@	inf	(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
1.0ms	x	@	inf	(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)

rewrite355.0ms (1.9%)

Memory

64.6MiB live, 629.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 492×	`-lowering-.f32`
4 492×	`-lowering-.f64`
3 838×	`/-lowering-/.f32`
3 838×	`/-lowering-/.f64`
3 318×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	173
1	244	173
2	2366	173
0	8201	157

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 599

Calls

Call 1

Inputs
(* (+ x (+ x eps)) 1/2)
(+ eps 0)
(* (* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2))) -2)
(* (sin (* (+ eps 0) 1/2)) (sin (* (+ x (+ x eps)) 1/2)))
(+ (cos eps) -1)
(cos eps)
(* (sin x) (neg eps))
(sin x)
(neg eps)
(- (cos (+ x eps)) (+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1))
(cos (+ x eps))
(+ x eps)
(+ (* (* x x) (+ (* (* x x) (+ (* x (* x -1/720)) 1/24)) -1/2)) 1)
(* eps (+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(+ (* eps (* -1/2 (cos x))) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(* -1/2 (cos x))
(cos x)
(+ x (+ x eps))
(sin (* (+ x (+ x eps)) 1/2))
(sin (* (+ eps 0) 1/2))
(* x -1/720)
(+ (* x (* x -1/720)) 1/24)
(* eps 1/6)

Outputs
(+.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps)) (.f64 #s(literal 1/2 binary64) x))
(+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x)) (.f64 eps #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(+.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64)) (.f64 eps #s(literal 1/2 binary64)))
(fma.f64 x #s(literal 1/2 binary64) (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))
(fma.f64 (+.f64 x eps) #s(literal 1/2 binary64) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x eps) (*.f64 #s(literal 1/2 binary64) x))
(fma.f64 #s(literal 1/2 binary64) (+.f64 x x) (*.f64 eps #s(literal 1/2 binary64)))
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(+.f64 (.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (.f64 x #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (sin.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 x eps)))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (cos.f64 (.f64 #s(literal 1/2 binary64) x)) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x eps))) (sin.f64 (*.f64 #s(literal 1/2 binary64) x))))
(fma.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) (+.f64 x x))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 x #s(literal 1/2 binary64))) (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 x #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x eps) #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (cos.f64 (.f64 x #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x eps) #s(literal 1/2 binary64))) (sin.f64 (*.f64 x #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 (cos.f64 (.f64 (+.f64 x x) #s(literal 1/2 binary64))) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64)))) (.f64 #s(literal 1 binary64) (sin.f64 (.f64 eps #s(literal 1/2 binary64)))))
(+.f64 (.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(sin.f64 (*.f64 eps #s(literal 1/2 binary64)))
(fma.f64 #s(literal 0 binary64) (cos.f64 (.f64 eps #s(literal 1/2 binary64))) (.f64 #s(literal 1 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(fma.f64 (sin.f64 (.f64 eps #s(literal 1/2 binary64))) #s(literal 1 binary64) (.f64 (cos.f64 (*.f64 eps #s(literal 1/2 binary64))) #s(literal 0 binary64)))
(*.f64 x #s(literal -1/720 binary64))
(*.f64 #s(literal -1/720 binary64) x)
(+.f64 (.f64 (.f64 x x) #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
(+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64))))
(fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(fma.f64 (*.f64 x #s(literal -1/720 binary64)) x #s(literal 1/24 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (-.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))) (neg.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64))) (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)) (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64)))) (neg.f64 (-.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64)))))
(pow.f64 (/.f64 (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (.f64 x x) #s(literal -1/17280 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64))) #s(literal -1 binary64))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/373248000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal 1/576 binary64)) (.f64 (*.f64 x x) #s(literal -1/17280 binary64)))))
(.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/518400 binary64) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal -1/24 binary64))))
(+.f64 #s(literal 0 binary64) (*.f64 eps #s(literal 1/6 binary64)))
(+.f64 (*.f64 eps #s(literal 1/6 binary64)) #s(literal 0 binary64))
(fma.f64 eps #s(literal 1/6 binary64) #s(literal 0 binary64))
(fma.f64 #s(literal 1/6 binary64) eps #s(literal 0 binary64))
(/.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) eps)
(/.f64 (neg.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64)))) (neg.f64 eps))
(/.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps))) (.f64 eps eps))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/6 binary64)) (.f64 eps eps))
(/.f64 (neg.f64 (.f64 #s(literal 1/6 binary64) (.f64 eps (.f64 eps eps)))) (neg.f64 (.f64 eps eps)))
(/.f64 (neg.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/6 binary64))) (neg.f64 (.f64 eps eps)))
(*.f64 eps #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) eps)

simplify378.0ms (2.1%)

Memory

-13.5MiB live, 799.1MiB allocated

Algorithm

1×	egg-herbie

Rules

11 594×	`accelerator-lowering-fma.f32`
11 594×	`accelerator-lowering-fma.f64`
6 582×	`-lowering-.f32`
6 582×	`-lowering-.f64`
4 252×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	444	3824
1	1345	3665
2	3781	3615
0	8102	3349

Stop Event

1×	iter limit
1×	node limit

Counts

408 → 408

Calls

Call 1

Inputs
(* 1/2 eps)
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
x
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
(* x (+ 1 (* 1/2 (/ eps x))))
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
x
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(+ x (* 1/2 eps))
(* 1/2 eps)
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* eps (+ 1/2 (/ x eps)))
(* 1/2 eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
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 (* 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)))))
(* -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)
(* -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)))
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)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 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)
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (+ eps x)) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(* 1/720 (pow x 6))
(* (pow x 6) (- 1/720 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (/ 1/2 (pow x 4))) (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 6) (- (+ 1/720 (+ (/ 1/2 (pow x 4)) (/ (cos (- eps (* -1 x))) (pow x 6)))) (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6)))))
(- (cos x) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (+ (cos x) (* -1 (* eps (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (+ (cos x) (* eps (- (* -1/2 (* eps (cos x))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (+ (cos x) (* eps (- (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))) (sin x)))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (+ eps x)) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(- (cos (- x (* -1 eps))) (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(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)))
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
(+ 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)))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1/720 (pow x 6))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 6) (- (* 1/24 (/ 1 (pow x 2))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* (pow x 6) (- (+ (* 1/24 (/ 1 (pow x 2))) (/ 1 (pow x 6))) (+ 1/720 (/ 1/2 (pow x 4)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* -1/2 (* eps (cos x))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x))))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* 1/2 (cos x)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* (pow x 2) (+ 1/4 (* -1/48 (pow x 2)))) 1/2)
(- (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/1440 (pow x 2)) 1/48)))) 1/2)
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos x))
(* -1/2 (cos 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)
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)))
(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))))
(* 1/2 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))
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
(* -1/720 x)
1/24
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(+ 1/24 (* -1/720 (pow x 2)))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* -1/720 (pow x 2))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)

Outputs
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
x
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
(* x (+ 1 (* 1/2 (/ eps x))))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 eps x) x) x)
x
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
(* -1 (* x (- (* -1/2 (/ eps x)) 1)))
(fma.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) (neg.f64 x) x)
x
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(+ x (* 1/2 eps))
(fma.f64 #s(literal 1/2 binary64) eps x)
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* eps (+ 1/2 (/ x eps)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
(* -1 (* eps (- (* -1 (/ x eps)) 1/2)))
(*.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 x eps)))
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
eps
(* -1 (* eps (sin x)))
(*.f64 (sin.f64 x) (neg.f64 eps))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* eps (+ (* -2 (+ (* -1/16 (sin x)) (* -1/48 (sin x)))) (* 1/24 (* eps (cos x)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 (cos.f64 x) (fma.f64 #s(literal 1/24 binary64) (.f64 eps eps) #s(literal -1/2 binary64)))) (neg.f64 (sin.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- (* 2 x) (* -1 eps))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (pow (sin (* 1/2 eps)) 2))
(.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))
(+ (* -2 (* x (* (cos (* 1/2 eps)) (sin (* 1/2 eps))))) (* -2 (pow (sin (* 1/2 eps)) 2)))
(.f64 (.f64 #s(literal -2 binary64) (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))))
(+ (* -2 (pow (sin (* 1/2 eps)) 2)) (* x (+ (* -2 (* (cos (* 1/2 eps)) (sin (* 1/2 eps)))) (* x (pow (sin (* 1/2 eps)) 2)))))
(fma.f64 x (.f64 (cos.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 #s(literal -2 binary64) (sin.f64 (.f64 #s(literal 1/2 binary64) eps)))) (.f64 (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)) (fma.f64 x x #s(literal -2 binary64))))
(+ (* -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))))))
(fma.f64 x (fma.f64 (.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (cos.f64 (.f64 #s(literal 1/2 binary64) eps))) (+.f64 #s(literal -2 binary64) (.f64 x (.f64 x #s(literal 1/3 binary64)))) (.f64 x (pow.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64)))) (.f64 #s(literal -2 binary64) (pow.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) #s(literal 2 binary64))))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (+ eps (* 2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (*.f64 (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)) #s(literal -2 binary64)))
(* -2 (* (sin (* 1/2 eps)) (sin (* 1/2 (- eps (* -2 x))))))
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(+ eps x)
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eps
(* eps (+ 1 (/ x eps)))
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(fma.f64 eps (/.f64 x eps) eps)
(* eps (+ 1 (/ x eps)))
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(* -1 (* eps (- (* -1 (/ x eps)) 1)))
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1
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(+ 1 (* -1/2 (pow x 2)))
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(* -1/2 (pow eps 2))
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(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
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(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
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(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
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(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
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(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
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(* eps (+ (* -1/2 (* eps (cos x))) (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
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(* -1 (sin x))
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(* 1/6 (* (pow eps 2) (sin x)))
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(* 1/6 (* (pow eps 2) (sin x)))
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(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.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 #s(literal 1/24 binary64) (.f64 x x) #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 x (.f64 x (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #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 (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* x (+ 2 (/ eps x)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ eps x)) 2)))
(*.f64 x (+.f64 (/.f64 eps x) #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
(+ eps (* 2 x))
(fma.f64 x #s(literal 2 binary64) eps)
eps
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* eps (+ 1 (* 2 (/ x eps))))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
eps
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) eps)
(* -1 (* eps (- (* -2 (/ x eps)) 1)))
(fma.f64 eps (/.f64 (*.f64 x #s(literal 2 binary64)) eps) 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 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 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (.f64 x #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)))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- eps (* -2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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 (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 eps (.f64 (sin.f64 x) #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 (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (+ eps (* 2 x))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(sin (* 1/2 (- (* 2 x) (* -1 eps))))
(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* -1/48 (pow eps 2))))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 1/3840 (pow eps 2)) 1/48))))
(.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 binary64))) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3840 (* -1/645120 (pow eps 2)))) 1/48))))
(.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 (* 1/2 eps))
(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))
(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))
(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))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(sin (* 1/2 eps))
(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
(* -1/720 x)
(*.f64 x #s(literal -1/720 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(+ 1/24 (* -1/720 (pow x 2)))
(fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64))
(* -1/720 (pow x 2))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* -1/720 (pow x 2))
(.f64 #s(literal -1/720 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* (pow x 2) (- (* 1/24 (/ 1 (pow x 2))) 1/720))
(.f64 x (.f64 x (+.f64 #s(literal -1/720 binary64) (/.f64 #s(literal 1/24 binary64) (*.f64 x x)))))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))
(* 1/6 eps)
(*.f64 eps #s(literal 1/6 binary64))

eval317.0ms (1.7%)

Memory: -34.9MiB live, 252.3MiB allocated
Compiler: Compiled 34 831 to 2 943 computations (91.6% saved)

prune160.0ms (0.9%)

Memory

27.6MiB live, 144.9MiB allocated

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	1 060	16	1 076
Fresh	2	1	3
Picked	3	2	5
Done	1	0	1
Total	1 066	19	1 085

Accuracy

100.0%

Counts

1 085 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps)))
	98.8%	(fma.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 x x) (.f64 eps (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))))))
	98.2%	(fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x (.f64 eps (.f64 eps #s(literal 1/4 binary64)))))))
▶	51.9%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
	80.8%	(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (neg.f64 eps))
	80.8%	(.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
	80.7%	(.f64 (fma.f64 x (.f64 x (*.f64 x #s(literal -1/6 binary64))) x) (neg.f64 eps))
	99.7%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 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 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.8%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	81.0%	(*.f64 (sin.f64 x) (neg.f64 eps))
	80.7%	(.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
	80.4%	(*.f64 x (neg.f64 eps))
▶	99.2%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	99.6%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
▶	98.8%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
▶	98.2%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	99.5%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))

Compiler

Compiled 650 to 410 computations (36.9% saved)

simplify467.0ms (2.5%)

Memory

-30.0MiB live, 335.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 1/4 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	cost-diff	0	(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	cost-diff	0	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
✓	cost-diff	64	(fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	cost-diff	320	(.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64))
✓	cost-diff	0	(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	cost-diff	0	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	cost-diff	192	(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	192	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	cost-diff	0	(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	cost-diff	320	(fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps)))

Rules

16 172×	`accelerator-lowering-fma.f32`
16 172×	`accelerator-lowering-fma.f64`
4 024×	`+-lowering-+.f64`
4 024×	`+-lowering-+.f32`
3 494×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	360
1	123	358
2	373	340
3	996	331
4	2594	327
5	4908	327
0	8122	295

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
x
(+ (* eps (* eps 1/6)) -1)
eps
(* eps 1/6)
1/6
-1
(* (* -1/2 (cos x)) (* eps eps))
(* -1/2 (cos x))
-1/2
(cos x)
(* eps eps)
(+ 1 -1)
1
-1
(* eps (+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1))))
eps
(+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1)))
-1/2
(* x (+ (* eps (* eps 1/6)) -1))
x
(+ (* eps (* eps 1/6)) -1)
(* eps 1/6)
1/6
-1
(* eps (+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1)))))
eps
(+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))))
-1/2
(* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1)))
x
(+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))
(+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))
(* (+ (* eps (* eps 1/6)) -1) -1/6)
(+ (* eps (* eps 1/6)) -1)
(* eps 1/6)
1/6
-1
-1/6
(* eps 1/4)
1/4
(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
eps
(+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(+ (* x (* x 1/4)) -1/2)
x
(* x 1/4)
1/4
-1/2
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
(+ (* eps (* eps 1/6)) -1)
(* eps 1/6)
1/6
-1

Outputs
(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)))))
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(sin x)
(sin.f64 x)
x
(+ (* eps (* eps 1/6)) -1)
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
eps
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)
(* (* -1/2 (cos x)) (* eps eps))
(.f64 (cos.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* -1/2 (cos x))
(*.f64 #s(literal -1/2 binary64) (cos.f64 x))
-1/2
#s(literal -1/2 binary64)
(cos x)
(cos.f64 x)
(* eps eps)
(*.f64 eps eps)
(+ 1 -1)
#s(literal 0 binary64)
1
#s(literal 1 binary64)
-1
#s(literal -1 binary64)
(* eps (+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 x (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) x))
eps
(+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1)))
(-.f64 (.f64 eps (fma.f64 x (.f64 eps #s(literal 1/6 binary64)) #s(literal -1/2 binary64))) x)
-1/2
#s(literal -1/2 binary64)
(* x (+ (* eps (* eps 1/6)) -1))
(.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
x
(+ (* eps (* eps 1/6)) -1)
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)
(* eps (+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1)))))
(.f64 eps (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))
eps
(+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))))
(fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))) (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
-1/2
#s(literal -1/2 binary64)
(* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1)))
(.f64 x (fma.f64 x (.f64 eps #s(literal 1/4 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)))))
x
(+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))
(fma.f64 x (.f64 eps #s(literal 1/4 binary64)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64))))
(+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))
(fma.f64 x (fma.f64 (.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))
(* (+ (* eps (* eps 1/6)) -1) -1/6)
(fma.f64 (*.f64 eps eps) #s(literal -1/36 binary64) #s(literal 1/6 binary64))
(+ (* eps (* eps 1/6)) -1)
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)
-1/6
#s(literal -1/6 binary64)
(* eps 1/4)
(*.f64 eps #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(.f64 eps (fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))))
eps
(+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(fma.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))))
(+ (* x (* x 1/4)) -1/2)
(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
x
(* x 1/4)
(*.f64 x #s(literal 1/4 binary64))
1/4
#s(literal 1/4 binary64)
-1/2
#s(literal -1/2 binary64)
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
(sin x)
(sin.f64 x)
(+ (* eps (* eps 1/6)) -1)
(fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))
(* eps 1/6)
(*.f64 eps #s(literal 1/6 binary64))
1/6
#s(literal 1/6 binary64)
-1
#s(literal -1 binary64)

localize152.0ms (0.8%)

Memory

30.4MiB live, 107.3MiB allocated

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	accuracy	99.8%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/6 binary64))
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	accuracy	99.8%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64))) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/6 binary64))
✓	accuracy	99.4%	(fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))
✓	accuracy	100.0%	(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	accuracy	100.0%	(.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	accuracy	99.8%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/6 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) #s(literal -1 binary64))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps)))
✓	accuracy	100.0%	(.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (*.f64 eps eps))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/6 binary64))

Samples

69.0ms	253×	0	valid
3.0ms	1×	3	valid
1.0ms	1×	2	valid
0.0ms	1×	1	valid

Compiler

Compiled 323 to 41 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-mult: 30.0ms (57.2% of total)

ival-add: 9.0ms (17.2% of total)

const: 7.0ms (13.4% of total)

ival-sin: 4.0ms (7.6% of total)

ival-cos: 2.0ms (3.8% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

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

series43.0ms (0.2%)

Memory

-8.9MiB live, 29.1MiB allocated

Counts

20 → 372

Calls

Call 1

Inputs
#<alt (+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))>
#<alt (* (sin x) (+ (* eps (* eps 1/6)) -1))>
#<alt (sin x)>
#<alt (+ (* eps (* eps 1/6)) -1)>
#<alt (+ 1 -1)>
#<alt (+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1)))>
#<alt (* eps (+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1))))>
#<alt (* x (+ (* eps (* eps 1/6)) -1))>
#<alt (* (+ (* eps (* eps 1/6)) -1) -1/6)>
#<alt (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))>
#<alt (* eps (+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1)))))>
#<alt (+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))))>
#<alt (* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1))))>
#<alt (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1)))>
#<alt (+ (* x (* x 1/4)) -1/2)>
#<alt (* x 1/4)>
#<alt (* eps 1/6)>
#<alt (* (* -1/2 (cos x)) (* eps eps))>
#<alt (cos x)>
#<alt (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))>

Outputs
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* eps (sin x)))>
#<alt (* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))>
#<alt (* 1/6 (* (pow eps 3) (sin x)))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))>
#<alt (* x (- (* 1/6 (pow eps 2)) 1))>
#<alt (* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* (sin x) (- (* 1/6 (pow eps 2)) 1))>
#<alt (* -1 (sin x))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* 1/6 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))>
#<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 -1>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (- (* 1/6 (pow eps 2)) 1)>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* 1/6 (pow eps 2))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))>
#<alt (* -1 x)>
#<alt (+ (* -1 x) (* -1/2 eps))>
#<alt (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))>
#<alt (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))>
#<alt (* 1/6 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* x (- (* 1/6 (pow eps 2)) 1))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (* 1/6 (pow eps 2)) 1))>
#<alt (* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))>
#<alt (* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))>
#<alt (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))>
#<alt (* 1/6 (* (pow eps 3) x))>
#<alt (* (pow eps 3) (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 3) x))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))>
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#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos x)))>
#<alt (* -1/2 (* (pow eps 2) (cos 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 (* 1/4 eps)>
#<alt (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))>
#<alt (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))>
#<alt (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))>
#<alt (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))>
#<alt (* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))>
#<alt (* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))>
#<alt (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* 1/6 x)>
#<alt (+ (* 1/6 x) (* 1/4 eps))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))>
#<alt (+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))>
#<alt (* -1/36 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))>
#<alt (* -1/36 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))>

Calls

93 calls:

Time	Variable		Point	Expression
14.0ms	eps	@	inf	(* (sin x) (+ (* eps (* eps 1/6)) -1))
5.0ms	x	@	0	(+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))
1.0ms	x	@	-inf	(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
1.0ms	x	@	inf	(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
1.0ms	eps	@	inf	(+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1)))

rewrite449.0ms (2.5%)

Memory

-7.6MiB live, 785.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 272×	`accelerator-lowering-fma.f32`
7 272×	`accelerator-lowering-fma.f64`
4 980×	`-lowering-.f32`
4 980×	`-lowering-.f64`
3 368×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	256
1	221	254
2	2080	254
0	8689	221

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 655

Calls

Call 1

Inputs
(+ (* (* (sin x) (+ (* eps (* eps 1/6)) -1)) eps) (* (* -1/2 (cos x)) (* eps eps)))
(* (sin x) (+ (* eps (* eps 1/6)) -1))
(sin x)
(+ (* eps (* eps 1/6)) -1)
(+ 1 -1)
(+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1)))
(* eps (+ (* eps -1/2) (* x (+ (* eps (* eps 1/6)) -1))))
(* x (+ (* eps (* eps 1/6)) -1))
(* (+ (* eps (* eps 1/6)) -1) -1/6)
(+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))
(* eps (+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1)))))
(+ (* eps -1/2) (* x (+ (* x (+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))) (+ (* eps (* eps 1/6)) -1))))
(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1))))
(+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (sin x) (+ (* eps (* eps 1/6)) -1)))
(+ (* x (* x 1/4)) -1/2)
(* x 1/4)
(* eps 1/6)
(* (* -1/2 (cos x)) (* eps eps))
(cos x)
(+ (* x (* (+ (* eps (* eps 1/6)) -1) -1/6)) (* eps 1/4))

Outputs
(+.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))
(+.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))
(-.f64 (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) (.f64 eps (-.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64)))))) (/.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) #s(literal 2 binary64)) (.f64 eps (-.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64)))))))
(-.f64 (/.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) #s(literal 2 binary64)) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))) (/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))))
(fma.f64 (sin.f64 x) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 eps (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 eps (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 #s(literal -1/2 binary64) (.f64 (cos.f64 x) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (cos.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps #s(literal -1/2 binary64))) eps (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal -1/2 binary64) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (*.f64 (sin.f64 x) eps)))
(fma.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (sin.f64 x) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(fma.f64 (.f64 eps (sin.f64 x)) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps))))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 eps (-.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (.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) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps))))) (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (-.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (.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) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (*.f64 eps eps))) #s(literal 2 binary64))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64))) (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps))))))
(/.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64))) (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))))))
(/.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (neg.f64 (pow.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) #s(literal 2 binary64)))) (.f64 eps (-.f64 (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 (cos.f64 x) (*.f64 eps #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))) (.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (-.f64 (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))) (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)))))))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 #s(literal 1/4 binary64) (pow.f64 (.f64 (cos.f64 x) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) (.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 (sin.f64 x) eps)) (.f64 (cos.f64 x) (.f64 #s(literal -1/2 binary64) (.f64 eps eps))))))))
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(fma.f64 (fma.f64 (.f64 eps (.f64 eps #s(literal 1/6 binary64))) #s(literal -1/6 binary64) #s(literal 1/6 binary64)) x (*.f64 eps #s(literal 1/4 binary64)))
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(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) #s(literal 1/36 binary64) (neg.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)))))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal -1/4 binary64) eps)))))
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(pow.f64 (/.f64 (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x #s(literal -1/6 binary64)) (.f64 #s(literal -1/4 binary64) eps)) (fma.f64 (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) #s(literal 1/36 binary64) (neg.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64))))) #s(literal -1 binary64))
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(.f64 (fma.f64 (.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))) #s(literal 1/36 binary64) (neg.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x #s(literal -1/6 binary64)) (*.f64 #s(literal -1/4 binary64) eps))))

simplify440.0ms (2.4%)

Memory

-20.6MiB live, 715.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12 464×	`accelerator-lowering-fma.f32`
12 464×	`accelerator-lowering-fma.f64`
7 570×	`-lowering-.f32`
7 570×	`-lowering-.f64`
2 938×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	484	5455
1	1553	5251
2	5381	5070
0	8310	4642

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

Inputs
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(* x (- (* 1/6 (pow eps 2)) 1))
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(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(* -1 (sin x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
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)
-1
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(- (* 1/6 (pow eps 2)) 1)
(* 1/6 (pow eps 2))
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(* 1/6 (* (pow eps 2) x))
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(* -1 (* x (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x)))))
(* -1 (* eps x))
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(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
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(* -1/2 (pow eps 2))
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(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
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(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
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(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (* 1/6 (pow eps 2)) 1))
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(* -1 x)
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(+ (* -1 x) (* 1/6 (* (pow eps 2) x)))
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(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)))
1/6
(+ 1/6 (* -1/36 (pow eps 2)))
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(* -1/36 (pow eps 2))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* -1/36 (pow eps 2))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(* (pow eps 2) (- (* 1/6 (/ 1 (pow eps 2))) 1/36))
(- (* 1/6 (pow eps 2)) 1)
(- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
(- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)
(* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* (pow x 2) (- (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* (pow x 2) (- (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/6 (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) x)) (* -1/4 eps)) x)) (* -1/6 (- (* 1/6 (pow eps 2)) 1))))
(- (* 1/6 (pow x 2)) 1)
(- (+ (* 1/6 (pow x 2)) (* 1/4 (* eps x))) 1)
(- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)
(- (+ (* 1/6 (pow x 2)) (* eps (+ (* 1/4 x) (* eps (+ 1/6 (* -1/36 (pow x 2))))))) 1)
(* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* (pow eps 2) (- (+ 1/6 (+ (* -1/36 (pow x 2)) (+ (* 1/6 (/ (pow x 2) (pow eps 2))) (* 1/4 (/ x eps))))) (/ 1 (pow eps 2))))
(* (pow eps 2) (+ 1/6 (* -1/36 (pow x 2))))
(* (pow eps 2) (+ 1/6 (+ (* -1/36 (pow x 2)) (* 1/4 (/ x eps)))))
(* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x)) eps)) (* -1/36 (pow x 2)))))
(* (pow eps 2) (+ 1/6 (+ (* -1 (/ (+ (* -1 (/ (- (* 1/6 (pow x 2)) 1) eps)) (* -1/4 x)) eps)) (* -1/36 (pow x 2)))))
(* 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)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* eps (+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* -1 (* (pow eps 3) (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (+ (* -1/4 (/ (pow x 2) eps)) (* 1/2 (/ 1 eps))))))
(* -1 (* (pow eps 3) (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (* -1 (/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (* x (+ 1/6 (* -1/36 (pow x 2))))) (* -1 (/ (+ (* -1 (+ 1/2 (* -1/4 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) eps)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/4 (/ (pow eps 2) x))))
(* (pow x 3) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 3) (+ (* -1/2 (/ (pow eps 2) (pow x 3))) (+ (* -1/6 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/4 (/ (pow eps 2) x)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* -1/6 (* eps (* (pow x 3) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* (pow x 3) (+ (* -1/4 (/ (pow eps 2) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* 1/4 (pow eps 2)) (/ (* eps (- (* 1/6 (pow eps 2)) 1)) x)) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/2 (/ (pow eps 2) x))) x)) (* 1/4 (pow eps 2))) x)) (* 1/6 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* 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)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(+ (* eps (- (+ (* 1/4 (pow x 2)) (* eps (* x (+ 1/6 (* -1/36 (pow x 2)))))) 1/2)) (* x (- (* 1/6 (pow x 2)) 1)))
(* (pow eps 2) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 2) (- (+ (* 1/4 (/ (pow x 2) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* 1/4 (/ (pow x 2) eps)) (+ (* x (+ 1/6 (* -1/36 (pow x 2)))) (/ (* x (- (* 1/6 (pow x 2)) 1)) (pow eps 2)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (* x (+ 1/6 (* -1/36 (pow x 2)))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (* -1/4 (pow x 2))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (+ (* -1 (/ (* x (- (* 1/6 (pow x 2)) 1)) eps)) (* -1/4 (pow x 2)))) eps)) (* x (+ 1/6 (* -1/36 (pow x 2))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* -1/6 (* (pow x 3) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 3) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* (pow x 3) (- (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x)))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ (* -1/2 (/ eps (pow x 3))) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/6 (/ (pow eps 2) (pow x 2))) (* 1/4 (/ eps x))))) (/ 1 (pow x 2))))
(* -1/6 (* (pow x 3) (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* (pow x 3) (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (- (+ (* 1/6 (/ (pow eps 2) x)) (* 1/4 eps)) (/ 1 x)) x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* (pow x 3) (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (- (* 1/6 (pow eps 2)) 1)) (* 1/2 (/ eps x))) x)) (* 1/4 eps)) x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* eps (sin x)))
(* eps (+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (+ (* 1/6 (* eps (sin x))) (* 1/4 (pow x 2))) 1/2))))
(* eps (+ (* -1 (sin x)) (* eps (- (+ (* 1/6 (* eps (sin x))) (* 1/4 (pow x 2))) 1/2))))
(* 1/6 (* (pow eps 3) (sin x)))
(* (pow eps 3) (- (+ (* 1/6 (sin x)) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* 1/6 (sin x)) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* 1/6 (sin x)) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 3) (sin x)))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 (sin x)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (sin x) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 (sin x)))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (+ (* -1/2 eps) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (+ (* -1/2 eps) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (+ (* -1/2 eps) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (pow x 2))))
(* 1/4 (* (pow eps 2) (pow x 2)))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (+ (* -1/2 eps) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (+ (* -1/2 eps) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (pow x 2))))
(* (pow x 2) (+ (* 1/4 (pow eps 2)) (/ (* eps (+ (* -1/2 eps) (* (sin x) (- (* 1/6 (pow eps 2)) 1)))) (pow x 2))))
(* -1 (sin x))
(+ (* -1 (sin x)) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 (sin x)) (* eps (- (+ (* 1/6 (* eps (sin x))) (* 1/4 (pow x 2))) 1/2)))
(+ (* -1 (sin x)) (* eps (- (+ (* 1/6 (* eps (sin x))) (* 1/4 (pow x 2))) 1/2)))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (- (+ (* 1/6 (sin x)) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* 1/6 (sin x)) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* 1/6 (sin x)) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 2) (sin x)))
(* (pow eps 2) (- (+ (* 1/6 (sin x)) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (/ (sin x) eps)) eps)) (* 1/6 (sin x))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/4 eps) (/ (* (sin x) (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/4 eps) (/ (* (sin x) (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/4 eps) (/ (* (sin x) (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* 1/4 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/4 eps) (/ (* (sin x) (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/4 eps) (/ (* (sin x) (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 2) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/4 eps) (/ (* (sin x) (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* 1/4 (* (pow eps 2) (pow x 2))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (* (pow eps 2) (pow x 2))) (* 1/4 (pow eps 2)))))
(+ (* -1/2 (pow eps 2)) (* (pow x 2) (+ (* 1/4 (pow eps 2)) (* (pow x 2) (+ (* -1/48 (pow eps 2)) (* 1/1440 (* (pow eps 2) (pow x 2))))))))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos x)))
(* -1/2 (* (pow eps 2) (cos 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)
(* 1/4 eps)
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(* 1/6 x)
(+ (* 1/6 x) (* 1/4 eps))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(* -1/36 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))

Outputs
(* -1/2 (pow eps 2))
(.f64 #s(literal -1/2 binary64) (.f64 eps eps))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(fma.f64 eps (.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))) (.f64 eps (.f64 x (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(fma.f64 eps (fma.f64 #s(literal -1/2 binary64) eps (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (.f64 (.f64 eps (fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (.f64 eps #s(literal 1/4 binary64)))) (.f64 x x)))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(+ (* -1/2 (* (pow eps 2) (cos x))) (* eps (* (sin x) (- (* 1/6 (pow eps 2)) 1))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -1/2 (cos x)) (* 1/6 (* eps (sin x)))))))
(.f64 eps (fma.f64 #s(literal -1/2 binary64) (.f64 eps (cos.f64 x)) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 eps eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* (pow eps 3) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* (pow eps 3) (+ (* -1 (/ (sin x) (pow eps 2))) (+ (* -1/2 (/ (cos x) eps)) (* 1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* 1/6 (* (pow eps 3) (sin x)))
(.f64 (.f64 eps eps) (.f64 eps (.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1/6 (sin x)) (* 1/2 (/ (cos x) eps)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) eps) (.f64 #s(literal 1/6 binary64) (sin.f64 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (+ (* -1 (/ (sin x) eps)) (* -1/2 (cos x))) eps)) (* -1/6 (sin x)))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (cos.f64 x) (/.f64 #s(literal -1/2 binary64) eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps))))))
(* x (- (* 1/6 (pow eps 2)) 1))
(.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))
(* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))
(.f64 x (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x (.f64 x (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)))) (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) #s(literal -1 binary64))))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))
(.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) (fma.f64 (.f64 x x) (fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64) (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))))) #s(literal -1 binary64))))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* (sin x) (- (* 1/6 (pow eps 2)) 1))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* -1 (sin x))
(neg.f64 (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(+ (* -1 (sin x)) (* 1/6 (* (pow eps 2) (sin x))))
(.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 (.f64 eps eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* 1/6 (* (pow eps 2) (sin x)))
(.f64 (.f64 eps eps) (*.f64 #s(literal 1/6 binary64) (sin.f64 x)))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* (pow eps 2) (+ (* -1 (/ (sin x) (pow eps 2))) (* 1/6 (sin x))))
(.f64 (.f64 eps eps) (.f64 (sin.f64 x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 x (.f64 x #s(literal -1/6 binary64))) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (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)) (.f64 x (.f64 x x)) x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
-1
#s(literal -1 binary64)
(- (* 1/6 (pow eps 2)) 1)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(- (* 1/6 (pow eps 2)) 1)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(- (* 1/6 (pow eps 2)) 1)
(fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64))
(* 1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))))
(* 1/6 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 1/6 binary64))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 1/6 (/ 1 (pow eps 2))))
(.f64 eps (.f64 eps (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (*.f64 eps eps)))))
(* -1 x)
(neg.f64 x)
(+ (* -1 x) (* -1/2 eps))
(-.f64 (*.f64 #s(literal -1/2 binary64) eps) x)
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))
(+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2)))
(fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))
(* 1/6 (* (pow eps 2) x))
(.f64 eps (.f64 x (*.f64 eps #s(literal 1/6 binary64))))
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(.f64 eps (.f64 eps (fma.f64 x #s(literal 1/6 binary64) (/.f64 #s(literal -1/2 binary64) eps))))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
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(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x 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)
(* 1/4 eps)
(*.f64 eps #s(literal 1/4 binary64))
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))
(+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps))
(fma.f64 x (.f64 (fma.f64 (.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64)))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))))
(* x (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/4 (/ eps x))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))))
(* -1/6 (* x (- (* 1/6 (pow eps 2)) 1)))
(.f64 x (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64)))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))))
(* -1 (* x (+ (* -1/4 (/ eps x)) (* 1/6 (- (* 1/6 (pow eps 2)) 1)))))
(.f64 x (fma.f64 eps (/.f64 #s(literal 1/4 binary64) x) (.f64 (fma.f64 (*.f64 eps eps) #s(literal 1/6 binary64) #s(literal -1 binary64)) #s(literal -1/6 binary64))))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(+ (* 1/6 x) (* 1/4 eps))
(fma.f64 eps #s(literal 1/4 binary64) (*.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(fma.f64 eps (fma.f64 eps (.f64 x #s(literal -1/36 binary64)) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))
(+ (* 1/6 x) (* eps (+ 1/4 (* -1/36 (* eps x)))))
(fma.f64 eps (fma.f64 eps (.f64 x #s(literal -1/36 binary64)) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/6 binary64)))
(* -1/36 (* (pow eps 2) x))
(.f64 eps (.f64 x (*.f64 eps #s(literal -1/36 binary64))))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(.f64 (.f64 (fma.f64 x #s(literal -1/36 binary64) (/.f64 #s(literal 1/4 binary64) eps)) eps) eps)
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(.f64 (.f64 eps eps) (fma.f64 x (+.f64 #s(literal -1/36 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/4 binary64) eps)))
(* (pow eps 2) (+ (* -1/36 x) (+ (* 1/6 (/ x (pow eps 2))) (* 1/4 (/ 1 eps)))))
(.f64 (.f64 eps eps) (fma.f64 x (+.f64 #s(literal -1/36 binary64) (/.f64 #s(literal 1/6 binary64) (*.f64 eps eps))) (/.f64 #s(literal 1/4 binary64) eps)))
(* -1/36 (* (pow eps 2) x))
(.f64 eps (.f64 x (*.f64 eps #s(literal -1/36 binary64))))
(* (pow eps 2) (+ (* -1/36 x) (* 1/4 (/ 1 eps))))
(.f64 (.f64 (fma.f64 x #s(literal -1/36 binary64) (/.f64 #s(literal 1/4 binary64) eps)) eps) eps)
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(.f64 (.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/36 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (/.f64 x eps) #s(literal -1/4 binary64)) eps)))
(* (pow eps 2) (+ (* -1 (/ (- (* -1/6 (/ x eps)) 1/4) eps)) (* -1/36 x)))
(.f64 (.f64 eps eps) (-.f64 (*.f64 x #s(literal -1/36 binary64)) (/.f64 (fma.f64 #s(literal -1/6 binary64) (/.f64 x eps) #s(literal -1/4 binary64)) eps)))

eval175.0ms (1%)

Memory: 18.1MiB live, 242.0MiB allocated
Compiler: Compiled 62 656 to 3 839 computations (93.9% saved)

prune135.0ms (0.7%)

Memory

-9.9MiB live, 207.2MiB allocated

Pruning

25 alts after pruning (22 fresh and 3 done)

	Pruned	Kept	Total
New	1 295	13	1 308
Fresh	3	9	12
Picked	4	1	5
Done	0	2	2
Total	1 302	25	1 327

Accuracy

100.0%

Counts

1 327 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(fma.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) (.f64 x eps) (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
	98.4%	(fma.f64 (.f64 x (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))) eps (.f64 #s(literal -1/2 binary64) (.f64 eps eps)))
▶	80.8%	(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (neg.f64 eps))
	80.8%	(.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
	99.7%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 1/3840 binary64)) #s(literal -1/48 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 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (*.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
	99.4%	(.f64 (.f64 (.f64 #s(literal 1/2 binary64) eps) (sin.f64 (.f64 (+.f64 x (+.f64 x eps)) #s(literal 1/2 binary64)))) #s(literal -2 binary64))
▶	99.8%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	81.0%	(*.f64 (sin.f64 x) (neg.f64 eps))
	80.7%	(.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
	80.4%	(*.f64 x (neg.f64 eps))
▶	99.0%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (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)) (.f64 x (.f64 x x)) x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	99.0%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	98.8%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))))
	99.2%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 (sin.f64 x))))
▶	98.2%	(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
✓	99.6%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	98.8%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
	98.8%	(.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)))))
✓	98.2%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	98.7%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))
	98.2%	(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
	99.5%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	80.7%	(.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
▶	51.9%	#s(literal 0 binary64)

Compiler

Compiled 807 to 520 computations (35.6% saved)

simplify412.0ms (2.2%)

Memory

-0.2MiB live, 391.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x #s(literal 1/4 binary64))
✓	cost-diff	(fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	(fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (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)) (.f64 x (.f64 x x)) x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64))))
✓	cost-diff	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (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)) (.f64 x (.f64 x x)) x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
✓	cost-diff	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
✓	cost-diff	(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (neg.f64 eps))
✓	cost-diff	(*.f64 x #s(literal 1/6 binary64))
✓	cost-diff	(fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	(fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))
✓	cost-diff	(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
✓	cost-diff	(*.f64 #s(literal 1/2 binary64) eps)
✓	cost-diff	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
✓	cost-diff	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))
✓	cost-diff	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))

Rules

22 786×	`accelerator-lowering-fma.f32`
22 786×	`accelerator-lowering-fma.f64`
4 842×	`-lowering-.f32`
4 842×	`-lowering-.f64`
3 878×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	312
1	140	312
2	404	312
3	1292	312
4	5771	311
0	8070	276

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) -2)
(* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x)))
(sin (* 1/2 eps))
(* 1/2 eps)
1/2
eps
(sin (+ (* 1/2 eps) x))
(+ (* 1/2 eps) x)
x
-2
0
(* eps (+ (* eps (+ (* eps (* x 1/6)) -1/2)) (neg x)))
eps
(+ (* eps (+ (* eps (* x 1/6)) -1/2)) (neg x))
(+ (* eps (* x 1/6)) -1/2)
(* x 1/6)
x
1/6
-1/2
(neg x)
(* (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x) (neg eps))
(+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x)
(+ (* (* x x) 1/120) -1/6)
(* x x)
x
1/120
-1/6
(* x (* x x))
(neg eps)
eps
(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))))
eps
(+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1)))
(+ (* x (* x 1/4)) -1/2)
x
(* x 1/4)
1/4
-1/2
(* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))
(+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x)
(+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6)
(* x x)
(+ (* (* x x) -1/5040) 1/120)
-1/5040
1/120
-1/6
(* x (* x x))
(+ (* eps (* eps 1/6)) -1)
(* eps 1/6)
1/6
-1

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

localize136.0ms (0.7%)

Memory

-12.3MiB live, 116.6MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 (fma.f64 (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)) (.f64 x (.f64 x x)) x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.8%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (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)) (.f64 x (.f64 x x)) x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
✓	accuracy	99.4%	(*.f64 eps #s(literal 1/6 binary64))
✓	accuracy	100.0%	(fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
✓	accuracy	100.0%	(fma.f64 (*.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64))
✓	accuracy	100.0%	(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (neg.f64 eps))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	100.0%	(neg.f64 x)
✓	accuracy	100.0%	(fma.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x))
✓	accuracy	99.8%	(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(sin.f64 (*.f64 #s(literal 1/2 binary64) eps))
✓	accuracy	100.0%	(.f64 (.f64 (sin.f64 (*.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	accuracy	100.0%	(sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))
✓	accuracy	99.8%	(.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) eps)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x)))

Samples

82.0ms	255×	0	valid
1.0ms	1×	3	valid

Compiler

Compiled 294 to 51 computations (82.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 31.0ms (51.8% of total)

const: 11.0ms (18.4% of total)

ival-add: 11.0ms (18.4% of total)

ival-sin: 4.0ms (6.7% of total)

ival-neg: 2.0ms (3.3% of total)

exact: 1.0ms (1.7% of total)

adjust: 0.0ms (0% of total)

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

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

series24.0ms (0.1%)

Memory

35.8MiB live, 35.8MiB allocated

Counts

21 → 372

Calls

Call 1

Inputs
#<alt (* (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) -2)>
#<alt (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x)))>
#<alt (sin (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ (* eps (+ (* eps (* x 1/6)) -1/2)) (neg x)))>
#<alt (+ (* eps (+ (* eps (* x 1/6)) -1/2)) (neg x))>
#<alt (+ (* eps (* x 1/6)) -1/2)>
#<alt (* x 1/6)>
#<alt (* (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x) (neg eps))>
#<alt (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x)>
#<alt (+ (* (* x x) 1/120) -1/6)>
#<alt (* x x)>
#<alt (* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))))>
#<alt (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1)))>
#<alt (+ (* x (* x 1/4)) -1/2)>
#<alt (* x 1/4)>
#<alt (sin (+ (* 1/2 eps) x))>
#<alt (neg x)>
#<alt (* x (* x x))>
#<alt (* eps 1/6)>
#<alt (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))>

Outputs
#<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 (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 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 (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))>
#<alt (* -2 (* (sin (* 1/2 eps)) (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 (* -1 (* eps x))>
#<alt (* eps (+ (* -1 x) (* -1/2 eps)))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))>
#<alt (* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))>
#<alt (* 1/6 (* (pow eps 3) x))>
#<alt (* (pow eps 3) (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 3) x))>
#<alt (* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* eps (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* eps (* x (+ 1 (* -1/6 (pow eps 2))))))>
#<alt (* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))>
#<alt (* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))>
#<alt (* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))>
#<alt (* -1 x)>
#<alt (- (* -1/2 eps) x)>
#<alt (- (* eps (- (* 1/6 (* eps x)) 1/2)) x)>
#<alt (- (* eps (- (* 1/6 (* eps x)) 1/2)) x)>
#<alt (* 1/6 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* x (- (* 1/6 (pow eps 2)) 1))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))>
#<alt (* -1 (* x (+ 1 (* -1/6 (pow eps 2)))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))>
#<alt -1/2>
#<alt (- (* 1/6 (* eps x)) 1/2)>
#<alt (- (* 1/6 (* eps x)) 1/2)>
#<alt (- (* 1/6 (* eps x)) 1/2)>
#<alt (* 1/6 (* eps x))>
#<alt (* eps (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* eps (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* eps (- (* 1/6 x) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* eps x))>
#<alt (* -1 (* eps (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))>
#<alt (* -1 (* eps (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))>
#<alt -1/2>
#<alt (- (* 1/6 (* eps x)) 1/2)>
#<alt (- (* 1/6 (* eps x)) 1/2)>
#<alt (- (* 1/6 (* eps x)) 1/2)>
#<alt (* 1/6 (* eps x))>
#<alt (* x (- (* 1/6 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (- (* 1/6 eps) (* 1/2 (/ 1 x))))>
#<alt (* x (- (* 1/6 eps) (* 1/2 (/ 1 x))))>
#<alt (* 1/6 (* eps x))>
#<alt (* -1 (* x (+ (* -1/6 eps) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1/6 eps) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1/6 eps) (* 1/2 (/ 1 x)))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<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) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))>
#<alt (* -1/120 (* eps (pow x 5)))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))>
#<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) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 5))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt (* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))>
#<alt -1/6>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (- (* 1/120 (pow x 2)) 1/6)>
#<alt (* 1/120 (pow x 2))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 2))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (* eps (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (* 1/4 (pow x 2)) 1/2))))>
#<alt (* eps (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2))))>
#<alt (* eps (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2))))>
#<alt (* 1/6 (* (pow eps 3) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (* (pow eps 3) (- (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 3) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 3) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))>
#<alt (* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))>
#<alt (* -1/5040 (* eps (* (pow x 7) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* (pow x 7) (+ (* -1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))>
#<alt (* (pow x 7) (+ (* -1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4))) (+ (* -1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))>
#<alt (* (pow x 7) (+ (* -1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4))) (+ (* -1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 5)))))))>
#<alt (* -1/5040 (* eps (* (pow x 7) (- (* 1/6 (pow eps 2)) 1))))>
#<alt (* -1 (* (pow x 7) (+ (* -1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (* 1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))))))>
#<alt (* -1 (* (pow x 7) (+ (* -1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (+ (* 1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4)))))))>
#<alt (* -1 (* (pow x 7) (+ (* -1/4 (/ (pow eps 2) (pow x 5))) (+ (* -1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (+ (* 1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4))))))))>
#<alt (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (* 1/4 (pow x 2)) 1/2)))>
#<alt (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2)))>
#<alt (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2)))>
#<alt (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))>
#<alt (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (* (pow eps 2) (- (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (+ (/ x eps) (/ (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) eps))) eps)) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (+ (/ x eps) (/ (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) eps))) eps)) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* -1/2 eps)>
#<alt (+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))>
#<alt (+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))>
#<alt (* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* (pow x 7) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2)))))>
#<alt (* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))))))>
#<alt (* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/4 (/ eps (pow x 5)))))))>
#<alt (* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/5040 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4)))))))>
#<alt (* -1 (* (pow x 7) (+ (* -1/4 (/ eps (pow x 5))) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))))))))>
#<alt -1/2>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (- (* 1/4 (pow x 2)) 1/2)>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 x)>
#<alt (* 1/4 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 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (* -1 x)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* 1/6 eps)>
#<alt (* x (- (* 1/6 (pow eps 2)) 1))>
#<alt (* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))>
#<alt (* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))>
#<alt (* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* (pow x 7) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2)))))>
#<alt (* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))))))>
#<alt (* (pow x 7) (- (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/6 (/ (pow eps 2) (pow x 6)))))) (/ 1 (pow x 6))))>
#<alt (* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))>
#<alt (* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/5040 (- (* 1/6 (pow eps 2)) 1)))))>
#<alt (* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4)))))))>
#<alt (* -1 (* (pow x 7) (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 6))) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))))))))>
#<alt (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>
#<alt (* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))>

Calls

93 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	0	(* (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x) (neg eps))
1.0ms	eps	@	0	(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))))
1.0ms	x	@	inf	(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))))
1.0ms	x	@	-inf	(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))))
1.0ms	x	@	-inf	(* (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x) (neg eps))

rewrite494.0ms (2.7%)

Memory

-0.6MiB live, 677.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 840×	`accelerator-lowering-fma.f32`
6 840×	`accelerator-lowering-fma.f64`
5 536×	`-lowering-.f32`
5 536×	`-lowering-.f64`
4 274×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	231
1	282	231
2	2437	231
0	10048	203

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 738

Calls

Call 1

Inputs
(* (* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x))) -2)
(* (sin (* 1/2 eps)) (sin (+ (* 1/2 eps) x)))
(sin (* 1/2 eps))
(* 1/2 eps)
(* eps (+ (* eps (+ (* eps (* x 1/6)) -1/2)) (neg x)))
(+ (* eps (+ (* eps (* x 1/6)) -1/2)) (neg x))
(+ (* eps (* x 1/6)) -1/2)
(* x 1/6)
(* (+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x) (neg eps))
(+ (* (+ (* (* x x) 1/120) -1/6) (* x (* x x))) x)
(+ (* (* x x) 1/120) -1/6)
(* x x)
(* eps (+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))))
(+ (* eps (+ (* x (* x 1/4)) -1/2)) (* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1)))
(+ (* x (* x 1/4)) -1/2)
(* x 1/4)
(sin (+ (* 1/2 eps) x))
(neg x)
(* x (* x x))
(* eps 1/6)
(* (+ (* (+ (* (* x x) (+ (* (* x x) -1/5040) 1/120)) -1/6) (* x (* x x))) x) (+ (* eps (* eps 1/6)) -1))

Outputs
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(/.f64 (.f64 (-.f64 (cos.f64 (-.f64 (.f64 #s(literal 1/2 binary64) eps) (fma.f64 #s(literal 1/2 binary64) eps x))) (cos.f64 (fma.f64 #s(literal 1/2 binary64) eps (fma.f64 #s(literal 1/2 binary64) eps x)))) #s(literal -2 binary64)) #s(literal 2 binary64))
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(.f64 (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) x) (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 1/6 binary64) (.f64 eps eps) #s(literal -1 binary64)) (fma.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) x))

simplify459.0ms (2.5%)

Memory

5.9MiB live, 201.2MiB allocated

Algorithm

1×	egg-herbie

Rules

11 418×	`accelerator-lowering-fma.f32`
11 418×	`accelerator-lowering-fma.f64`
6 814×	`-lowering-.f32`
6 814×	`-lowering-.f64`
2 796×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	504	5404
1	1652	5215
2	5503	4865
0	8160	4425

Stop Event

1×	iter limit
1×	node limit

Counts

372 → 372

Calls

Call 1

Inputs
(* -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 (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 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 (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- (* 1/2 eps) (* -1 x)))))
(* -2 (* (sin (* 1/2 eps)) (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)
(* -1 (* eps x))
(* eps (+ (* -1 x) (* -1/2 eps)))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* eps (+ (* -1 x) (* eps (- (* 1/6 (* eps x)) 1/2))))
(* 1/6 (* (pow eps 3) x))
(* (pow eps 3) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 3) x))
(* -1 (* (pow eps 3) (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* -1 (/ x eps)) 1/2) eps)) (* -1/6 x))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(* eps (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* x (+ (* -1/2 (/ (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* eps (* x (+ 1 (* -1/6 (pow eps 2))))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
(* -1 (* x (+ (* 1/2 (/ (pow eps 2) x)) (* eps (+ 1 (* -1/6 (pow eps 2)))))))
(* -1 x)
(- (* -1/2 eps) x)
(- (* eps (- (* 1/6 (* eps x)) 1/2)) x)
(- (* eps (- (* 1/6 (* eps x)) 1/2)) x)
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ x (pow eps 2))) (* 1/6 x)) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 2) x))
(* (pow eps 2) (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(* (pow eps 2) (+ (* -1 (/ (+ 1/2 (/ x eps)) eps)) (* 1/6 x)))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(* x (- (+ (* -1/2 (/ eps x)) (* 1/6 (pow eps 2))) 1))
(* -1 (* x (+ 1 (* -1/6 (pow eps 2)))))
(* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))
(* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))
(* -1 (* x (+ 1 (+ (* -1/6 (pow eps 2)) (* 1/2 (/ eps x))))))
-1/2
(- (* 1/6 (* eps x)) 1/2)
(- (* 1/6 (* eps x)) 1/2)
(- (* 1/6 (* eps x)) 1/2)
(* 1/6 (* eps x))
(* eps (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* eps (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* eps (- (* 1/6 x) (* 1/2 (/ 1 eps))))
(* 1/6 (* eps x))
(* -1 (* eps (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))
(* -1 (* eps (+ (* -1/6 x) (* 1/2 (/ 1 eps)))))
-1/2
(- (* 1/6 (* eps x)) 1/2)
(- (* 1/6 (* eps x)) 1/2)
(- (* 1/6 (* eps x)) 1/2)
(* 1/6 (* eps x))
(* x (- (* 1/6 eps) (* 1/2 (/ 1 x))))
(* x (- (* 1/6 eps) (* 1/2 (/ 1 x))))
(* x (- (* 1/6 eps) (* 1/2 (/ 1 x))))
(* 1/6 (* eps x))
(* -1 (* x (+ (* -1/6 eps) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1/6 eps) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1/6 eps) (* 1/2 (/ 1 x)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* -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) (+ (* -1/120 (* eps (pow x 2))) (* 1/6 eps)))))
(* -1/120 (* eps (pow x 5)))
(* (pow x 5) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2)))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* (pow x 5) (+ (* -1 (/ eps (pow x 4))) (+ (* -1/120 eps) (* 1/6 (/ eps (pow x 2))))))
(* -1/120 (* eps (pow x 5)))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (* 1/120 eps))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* -1 (* (pow x 5) (+ (* -1/6 (/ eps (pow x 2))) (+ (* 1/120 eps) (/ eps (pow x 4))))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
(* -1 (* eps (+ x (* (pow x 3) (- (* 1/120 (pow x 2)) 1/6)))))
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) (- (* 1/120 (pow x 2)) 1/6))))
(* 1/120 (pow x 5))
(* (pow x 5) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 5) (- (+ 1/120 (/ 1 (pow x 4))) (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 5))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) 1/120)))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
(* -1 (* (pow x 5) (- (* 1/6 (/ 1 (pow x 2))) (+ 1/120 (/ 1 (pow x 4))))))
-1/6
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(- (* 1/120 (pow x 2)) 1/6)
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 2))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/120 (* 1/6 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(* eps (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (* 1/4 (pow x 2)) 1/2))))
(* eps (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2))))
(* eps (+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2))))
(* 1/6 (* (pow eps 3) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(* (pow eps 3) (- (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 3) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 3) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (* 1/4 (pow x 2)) 1/2) eps)) (* -1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))
(* -1 (* (pow eps 3) (+ (* -1 (/ (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) eps)) (* 1/4 (pow x 2))) 1/2) eps)) (* -1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))))
(* -1/2 (pow eps 2))
(+ (* -1/2 (pow eps 2)) (* eps (* x (- (* 1/6 (pow eps 2)) 1))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* 1/4 (* (pow eps 2) x)) (* eps (- (* 1/6 (pow eps 2)) 1)))))
(+ (* -1/2 (pow eps 2)) (* x (+ (* eps (- (* 1/6 (pow eps 2)) 1)) (* x (+ (* -1/6 (* eps (* x (- (* 1/6 (pow eps 2)) 1)))) (* 1/4 (pow eps 2)))))))
(* -1/5040 (* eps (* (pow x 7) (- (* 1/6 (pow eps 2)) 1))))
(* (pow x 7) (+ (* -1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2)))))
(* (pow x 7) (+ (* -1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4))) (+ (* -1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))))))
(* (pow x 7) (+ (* -1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4))) (+ (* -1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (+ (* 1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (* 1/4 (/ (pow eps 2) (pow x 5)))))))
(* -1/5040 (* eps (* (pow x 7) (- (* 1/6 (pow eps 2)) 1))))
(* -1 (* (pow x 7) (+ (* -1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (* 1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))))))
(* -1 (* (pow x 7) (+ (* -1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (+ (* 1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4)))))))
(* -1 (* (pow x 7) (+ (* -1/4 (/ (pow eps 2) (pow x 5))) (+ (* -1/120 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 2))) (+ (* 1/5040 (* eps (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (/ (* eps (- (* 1/6 (pow eps 2)) 1)) (pow x 4))))))))
(* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (* 1/4 (pow x 2)) 1/2)))
(+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2)))
(+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* eps (- (+ (* 1/6 (* eps (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))) (* 1/4 (pow x 2))) 1/2)))
(* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(* (pow eps 2) (- (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (- (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps)))) (* 1/2 (/ 1 eps))))
(* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(* (pow eps 2) (- (+ (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/4 (/ (pow x 2) eps))) (* 1/2 (/ 1 eps))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (+ (/ x eps) (/ (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) eps))) eps)) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* (pow eps 2) (+ (* -1 (/ (+ (* -1 (- (* 1/4 (pow x 2)) 1/2)) (+ (/ x eps) (/ (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)) eps))) eps)) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* -1/2 eps)
(+ (* -1/2 eps) (* x (- (* 1/6 (pow eps 2)) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* 1/4 (* eps x))) 1)))
(+ (* -1/2 eps) (* x (- (+ (* 1/6 (pow eps 2)) (* x (+ (* -1/6 (* x (- (* 1/6 (pow eps 2)) 1))) (* 1/4 eps)))) 1)))
(* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 7) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2)))))
(* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))))))
(* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/4 (/ eps (pow x 5)))))))
(* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/5040 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4)))))))
(* -1 (* (pow x 7) (+ (* -1/4 (/ eps (pow x 5))) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))))))))
-1/2
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(- (* 1/4 (pow x 2)) 1/2)
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* 1/4 (pow x 2))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/4 (* 1/2 (/ 1 (pow x 2)))))
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 x)
(* 1/4 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 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* 1/6 eps)
(* x (- (* 1/6 (pow eps 2)) 1))
(* x (- (+ (* -1/6 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/6 (pow eps 2))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1)))))) 1))
(* x (- (+ (* 1/6 (pow eps 2)) (* (pow x 2) (+ (* -1/6 (- (* 1/6 (pow eps 2)) 1)) (* (pow x 2) (+ (* -1/5040 (* (pow x 2) (- (* 1/6 (pow eps 2)) 1))) (* 1/120 (- (* 1/6 (pow eps 2)) 1))))))) 1))
(* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))
(* (pow x 7) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2)))))
(* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))))))
(* (pow x 7) (- (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/6 (/ (pow eps 2) (pow x 6)))))) (/ 1 (pow x 6))))
(* -1/5040 (* (pow x 7) (- (* 1/6 (pow eps 2)) 1)))
(* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/5040 (- (* 1/6 (pow eps 2)) 1)))))
(* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4)))))))
(* -1 (* (pow x 7) (+ (* -1 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 6))) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))))))))
(* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(+ (* -1 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))) (* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* 1/6 (* (pow eps 2) (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6)))))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))

Outputs
(* -1 (* eps (sin x)))
(neg.f64 (*.f64 eps (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* -1/2 (* eps (cos x)))))
(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
(* eps (+ (* -1 (sin x)) (* eps (+ (* -2 (* eps (+ (* -1/16 (sin x)) (* -1/48 (sin x))))) (* -1/2 (cos x))))))
(.f64 eps (-.f64 (.f64 eps (fma.f64 eps (.f64 (sin.f64 x) #s(literal 1/6 binary64)) (.f64 #s(literal -1/2 binary64) (cos.f64 x)))) (sin.f64 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)))))))))
(.f64 eps (fma.f64 eps (fma.f64 eps (fma.f64 eps (.f64 (cos.f64 x) #s(literal 1/24 binary64)) (.f64 (sin.f64 x) #s(literal 1/6 binary64))) (.f64 #s(literal -1/2 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (+ x (* 1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
(.f64 (sin.f64 (fma.f64 eps #s(literal 1/2 binary64) x)) (.f64 #s(literal -2 binary64) (sin.f64 (*.f64 eps #s(literal 1/2 binary64)))))
(* -2 (* (sin (* 1/2 eps)) (sin (- x (* -1/2 eps)))))
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(* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))))))
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(* (pow x 7) (+ (* -1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4))) (+ (* -1/5040 (- (* 1/6 (pow eps 2)) 1)) (+ (* 1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (* 1/4 (/ eps (pow x 5)))))))
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(* -1 (* (pow x 7) (+ (* -1/120 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 2))) (+ (* 1/5040 (- (* 1/6 (pow eps 2)) 1)) (* 1/6 (/ (- (* 1/6 (pow eps 2)) 1) (pow x 4)))))))
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(.f64 (.f64 eps eps) (.f64 (fma.f64 x (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))
(* (pow eps 2) (+ (* -1 (/ (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) (pow eps 2))) (* 1/6 (+ x (* (pow x 3) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
(.f64 (.f64 eps eps) (.f64 (fma.f64 x (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) x) (+.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -1 binary64) (.f64 eps eps)))))

eval239.0ms (1.3%)

Memory: -18.5MiB live, 216.7MiB allocated
Compiler: Compiled 88 300 to 3 670 computations (95.8% saved)

prune142.0ms (0.8%)

Memory

-2.3MiB live, 203.0MiB allocated

Pruning

24 alts after pruning (17 fresh and 7 done)

	Pruned	Kept	Total
New	1 244	6	1 250
Fresh	6	11	17
Picked	1	4	5
Done	0	3	3
Total	1 251	24	1 275

Accuracy

100.0%

Counts

1 275 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.2%	(fma.f64 (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (.f64 eps eps) (*.f64 eps (neg.f64 x)))
	98.4%	(fma.f64 (neg.f64 x) eps (.f64 eps (.f64 eps (fma.f64 eps (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))))
✓	80.8%	(.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (neg.f64 eps))
	80.8%	(.f64 (fma.f64 (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x) (neg.f64 eps))
	99.8%	(.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 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	99.7%	(.f64 (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/48 binary64)) #s(literal 1/2 binary64))) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
	99.5%	(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps x))) #s(literal -2 binary64))
✓	81.0%	(*.f64 (sin.f64 x) (neg.f64 eps))
	80.7%	(.f64 x (.f64 eps (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
	80.4%	(*.f64 x (neg.f64 eps))
✓	99.0%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (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)) (.f64 x (.f64 x x)) x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	99.0%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 (fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	98.8%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal -1 binary64)))))
	99.0%	(.f64 eps (fma.f64 eps (fma.f64 x (.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (neg.f64 (fma.f64 x (.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (.f64 x x) #s(literal -1/5040 binary64) #s(literal 1/120 binary64))) #s(literal -1/6 binary64))) x))))
✓	98.2%	(.f64 eps (fma.f64 eps (fma.f64 eps (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (neg.f64 x)))
✓	99.6%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (cos.f64 x)) (.f64 (sin.f64 x) (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	98.8%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 x (fma.f64 x (.f64 (fma.f64 eps (.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)) #s(literal -1/6 binary64)) (*.f64 eps #s(literal 1/4 binary64))) #s(literal -1 binary64)))))
	98.8%	(.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)))))
✓	98.2%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 binary64)))))
	98.7%	(.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64)))))
	98.2%	(*.f64 eps (fma.f64 eps #s(literal -1/2 binary64) (neg.f64 x)))
	99.5%	(.f64 eps (-.f64 (.f64 eps (*.f64 #s(literal -1/2 binary64) (cos.f64 x))) (sin.f64 x)))
	80.7%	(.f64 eps (.f64 x (fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal -1 binary64))))
✓	51.9%	#s(literal 0 binary64)

Compiler

Compiled 1 101 to 441 computations (59.9% saved)

regimes34.0ms (0.2%)

Memory

-1.0MiB live, 38.5MiB allocated

Counts

44 → 1

Calls

Call 1

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

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

Calls

3 calls:

12.0ms	x
11.0ms	eps
9.0ms	(-.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)

regimes34.0ms (0.2%)

Memory

-3.4MiB live, 36.7MiB allocated

Counts

43 → 1

Calls

Call 1

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

Calls

3 calls:

12.0ms	x
11.0ms	eps
9.0ms	(-.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)

regimes28.0ms (0.2%)

Memory

-9.6MiB live, 30.0MiB allocated

Counts

36 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

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)

regimes26.0ms (0.1%)

Memory

0.2MiB live, 40.0MiB allocated

Counts

32 → 1

Calls

Call 1

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

Outputs
(.f64 (.f64 (*.f64 eps #s(literal 1/2 binary64)) (sin.f64 (fma.f64 #s(literal 1/2 binary64) eps 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
99.5%	1	`x`
99.5%	1	`eps`
99.5%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes22.0ms (0.1%)

Memory

35.0MiB live, 35.0MiB allocated

Counts

28 → 1

Calls

Call 1

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

Outputs

(*.f64 eps (fma.f64 eps (fma.f64 x (*.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (*.f64 (fma.f64 (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)) (*.f64 x (*.f64 x x)) x) (fma.f64 eps (*.f64 eps #s(literal 1/6 binary64)) #s(literal -1 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
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes20.0ms (0.1%)

Memory

-4.6MiB live, 34.6MiB allocated

Counts

24 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes19.0ms (0.1%)

Memory

-10.5MiB live, 30.9MiB allocated

Counts

22 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

7.0ms	eps
6.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`eps`
99.0%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes18.0ms (0.1%)

Memory

-5.0MiB live, 34.4MiB allocated

Counts

21 → 1

Calls

Call 1

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

Outputs

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

Calls

3 calls:

7.0ms	eps
6.0ms	x
5.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes17.0ms (0.1%)

Memory

-10.6MiB live, 28.9MiB allocated

Counts

19 → 1

Calls

Call 1

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

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

Calls

3 calls:

6.0ms	eps
6.0ms	x
4.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.8%	1	`eps`
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
98.8%	1	`x`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes14.0ms (0.1%)

Memory

26.9MiB live, 26.9MiB allocated

Counts

16 → 1

Calls

Call 1

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

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
98.8%	1	`x`
98.8%	1	`eps`
98.8%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes13.0ms (0.1%)

Memory

-17.3MiB live, 22.3MiB allocated

Counts

14 → 1

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	eps
4.0ms	x
3.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.7%	1	`x`
98.7%	1	`eps`
98.7%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

3 calls:

3.0ms	x
3.0ms	eps
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`
98.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes9.0ms (0%)

Memory

-24.8MiB live, 16.6MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	eps
3.0ms	x
2.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
98.2%	1	`x`
98.2%	1	`eps`
98.2%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

12.0MiB live, 12.0MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

2.0ms	eps
2.0ms	x
1.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

Results

Accuracy	Segments	Branch
80.4%	1	`x`
80.4%	1	`eps`
80.4%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

8.4MiB live, 8.4MiB 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:

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

Results

Accuracy	Segments	Branch
51.9%	1	`(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))`
51.9%	1	`x`
51.9%	1	`eps`

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify12.0ms (0.1%)

Memory

-24.3MiB live, 15.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	89	255
1	135	255
2	146	255
3	152	255
4	153	255

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.5s (8.1%)

Memory

7.0MiB live, 206.4MiB allocated

Rules

14 158×	`accelerator-lowering-fma.f32`
14 158×	`accelerator-lowering-fma.f64`
12 464×	`accelerator-lowering-fma.f32`
12 464×	`accelerator-lowering-fma.f64`
11 594×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	50	16
2	376	16
3	4688	16
0	8201	16
0	504	5404
1	1652	5215
2	5503	4865
0	8160	4425
0	40	256
1	221	254
2	2080	254
0	8689	221
0	444	3824
1	1345	3665
2	3781	3615
0	8102	3349
0	484	5455
1	1553	5251
2	5381	5070
0	8310	4642
0	44	173
1	244	173
2	2366	173
0	8201	157
0	105	498
1	277	495
2	609	495
3	2398	494
4	7880	494
0	8026	474

Stop Event

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

Compiler

Compiled 667 to 379 computations (43.2% saved)

preprocess99.0ms (0.5%)

Memory: -1.9MiB live, 80.3MiB allocated
Compiler: Compiled 600 to 240 computations (60% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	21	48
1	43	44
2	87	42
3	160	42
4	287	42
5	387	42
6	478	42
7	543	42
8	556	42
9	566	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

Iter	Nodes	Cost
0	21	48
1	43	44
2	87	42
3	160	42
4	287	42
5	387	42
6	478	42
7	543	42
8	556	42
9	566	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18

analyze46.0ms (0.2%)

sample9.5s (51.7%)

preprocess29.0ms (0.2%)

explain224.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0%)

localize105.0ms (0.6%)

series4.0ms (0%)

rewrite299.0ms (1.6%)

simplify389.0ms (2.1%)

eval55.0ms (0.3%)

prune48.0ms (0.3%)

simplify375.0ms (2.1%)

localize384.0ms (2.1%)

series34.0ms (0.2%)

rewrite355.0ms (1.9%)

simplify378.0ms (2.1%)

eval317.0ms (1.7%)

prune160.0ms (0.9%)

simplify467.0ms (2.5%)

localize152.0ms (0.8%)

series43.0ms (0.2%)

rewrite449.0ms (2.5%)

simplify440.0ms (2.4%)

eval175.0ms (1%)

prune135.0ms (0.7%)

simplify412.0ms (2.2%)

localize136.0ms (0.7%)

series24.0ms (0.1%)

rewrite494.0ms (2.7%)

simplify459.0ms (2.5%)

eval239.0ms (1.3%)

prune142.0ms (0.8%)

regimes34.0ms (0.2%)

regimes34.0ms (0.2%)

regimes28.0ms (0.2%)

regimes26.0ms (0.1%)

regimes22.0ms (0.1%)

regimes20.0ms (0.1%)

regimes19.0ms (0.1%)

regimes18.0ms (0.1%)

regimes17.0ms (0.1%)

regimes14.0ms (0.1%)

regimes13.0ms (0.1%)

regimes9.0ms (0%)

regimes9.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

simplify12.0ms (0.1%)

soundness1.5s (8.1%)

preprocess99.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	21	48
1	43	44
2	87	42
3	160	42
4	287	42
5	387	42
6	478	42
7	543	42
8	556	42
9	566	42
0	6	7
1	9	7
2	14	7
3	20	7
4	28	7
5	43	7
6	76	7
7	101	7
8	144	7
9	159	7
10	167	7
0	167	7

Iter	Nodes	Cost
0	6	18
1	9	18
2	14	18
3	20	18
4	28	18
5	43	18
6	76	18
7	101	18
8	144	18
9	159	18
10	167	18
0	167	18