Metrics for 2sin (example 3.3)

analyze46.0ms (0.4%)

Memory

-29.5MiB live, 60.9MiB 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)

sample6.2s (48.5%)

Memory

-122.6MiB live, 8 208.4MiB allocated

Samples

3.5s	25 840×	0	invalid
702.0ms	5 449×	0	valid
481.0ms	2 807×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 3.3s

const: 993.0ms (29.9% of total)

ival-sin: 661.0ms (19.9% of total)

ival-mult: 283.0ms (8.5% of total)

ival-fabs: 278.0ms (8.4% of total)

ival-add: 266.0ms (8% of total)

ival-<=: 261.0ms (7.9% of total)

ival-<: 205.0ms (6.2% of total)

ival-sub: 176.0ms (5.3% of total)

ival-and: 98.0ms (2.9% of total)

adjust: 52.0ms (1.6% of total)

exact: 41.0ms (1.2% of total)

ival-assert: 12.0ms (0.4% of total)

Bogosity

preprocess25.0ms (0.2%)

Memory

1.8MiB live, 39.8MiB allocated

Algorithm

1×	egg-herbie

Rules

102×	`sub-neg`
80×	`accelerator-lowering-fma.f32`
80×	`accelerator-lowering-fma.f64`
68×	`cancel-sign-sub-inv`
64×	`associate--r+`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
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
(- (sin (+ x eps)) (sin x))

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

explain97.0ms (0.8%)

Memory

-25.3MiB live, 176.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
232	-	3	(-1.2733220219159224e-171 2.312485591617144e-173)	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`
0	-	0	-	`(sin.f64 (+.f64 x eps))`
0	-	0	-	`eps`
0	-	0	-	`(+.f64 x eps)`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))`	cancellation	229	5

Confusion

	Predicted +	Predicted -
+	229	3
-	0	24

Precision

1.0

Recall

0.9870689655172413

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	229	3	0
-	0	2	22

Precision?

0.9914529914529915

Recall?

1.0

Freqs

test

number	freq
0	27
1	229

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

24.0ms	316×	0	valid
18.0ms	188×	1	valid
2.0ms	6×	3	valid
2.0ms	2×	2	valid

Compiler

Compiled 58 to 28 computations (51.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sin: 19.0ms (65.8% of total)

adjust: 3.0ms (10.4% of total)

ival-add: 3.0ms (10.4% of total)

ival-sub: 3.0ms (10.4% 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

1.6MiB live, 1.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify8.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

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

localize28.0ms (0.2%)

Memory

13.5MiB live, 49.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

Samples

10.0ms	158×	0	valid
9.0ms	94×	1	valid
1.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sin: 8.0ms (61.7% of total)

adjust: 2.0ms (15.4% of total)

ival-add: 2.0ms (15.4% of total)

ival-sub: 2.0ms (15.4% of total)

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

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

series11.0ms (0.1%)

Memory

-32.9MiB live, 7.2MiB allocated

Counts

4 → 84

Calls

Call 1

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

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

Calls

21 calls:

Time	Variable		Point	Expression
8.0ms	x	@	0	(- (sin (+ x eps)) (sin x))
1.0ms	eps	@	inf	(- (sin (+ x eps)) (sin x))
0.0ms	eps	@	0	(- (sin (+ x eps)) (sin x))
0.0ms	x	@	0	(sin (+ x eps))
0.0ms	x	@	inf	(+ x eps)

rewrite344.0ms (2.7%)

Memory

-32.3MiB live, 513.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 986×	`accelerator-lowering-fma.f32`
4 986×	`accelerator-lowering-fma.f64`
4 676×	`-lowering-.f32`
4 676×	`-lowering-.f64`
2 176×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	49	16
2	376	16
3	4763	16
0	8212	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 214

Calls

Call 1

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

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

simplify527.0ms (4.1%)

Memory

27.7MiB live, 491.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16 678×	`accelerator-lowering-fma.f32`
16 678×	`accelerator-lowering-fma.f64`
4 132×	`-lowering-.f32`
4 132×	`-lowering-.f64`
2 614×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

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

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

eval54.0ms (0.4%)

Memory: 24.3MiB live, 62.8MiB allocated
Compiler: Compiled 7 797 to 843 computations (89.2% saved)

prune78.0ms (0.6%)

Memory

-24.8MiB live, 68.3MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	293	5	298
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	294	5	299

Accuracy

100.0%

Counts

299 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	60.2%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
▶	59.4%	(-.f64 (sin.f64 (+.f64 x eps)) x)
▶	100.0%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
▶	99.9%	(*.f64 eps (cos.f64 x))
▶	98.8%	(sin.f64 eps)

Compiler

Compiled 90 to 58 computations (35.6% saved)

simplify135.0ms (1.1%)

Memory

-5.4MiB live, 73.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	128	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
✓	cost-diff	0	(+.f64 x eps)
✓	cost-diff	0	(sin.f64 (+.f64 x eps))
✓	cost-diff	0	(-.f64 (sin.f64 (+.f64 x eps)) x)
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(*.f64 eps (cos.f64 x))
✓	cost-diff	0	(sin.f64 eps)
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
✓	cost-diff	0	(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))

Rules

1 504×	`accelerator-lowering-fma.f32`
1 504×	`accelerator-lowering-fma.f64`
864×	`-lowering-.f32`
864×	`-lowering-.f64`
368×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	46	92
2	94	92
3	201	92
4	361	92
5	569	92
6	844	92
7	977	92
8	1169	92
9	1566	92
10	1780	92
11	1980	92
12	2014	92
13	2019	92
14	2021	92
15	2024	92
0	2024	88

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize131.0ms (1%)

Memory

10.3MiB live, 49.2MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	60.4%	(-.f64 (sin.f64 (+.f64 x eps)) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))
✓	accuracy	100.0%	(+.f64 x eps)
✓	accuracy	100.0%	(sin.f64 (+.f64 x eps))
✓	accuracy	60.9%	(-.f64 (sin.f64 (+.f64 x eps)) x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(*.f64 eps (cos.f64 x))
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))

Samples

81.0ms	94×	1	valid
24.0ms	158×	0	valid
2.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 96 to 22 computations (77.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

const: 59.0ms (64.5% of total)

ival-mult: 11.0ms (12% of total)

ival-sin: 7.0ms (7.7% of total)

adjust: 4.0ms (4.4% of total)

ival-add: 4.0ms (4.4% of total)

ival-sub: 3.0ms (3.3% of total)

ival-cos: 2.0ms (2.2% of total)

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

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

exact: 0.0ms (0% of total)

series56.0ms (0.4%)

Memory

-22.2MiB live, 17.1MiB allocated

Counts

14 → 252

Calls

Call 1

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

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) (sin x)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps (sin x)))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (+ (cos x) (* -1/2 (* eps (sin x))))>
#<alt (* -1/2 x)>
#<alt (* x (- (* 1/12 (pow x 2)) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))>
#<alt (* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (sin x))>
#<alt (* -1/2 (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 eps>
#<alt (* eps (+ 1 (* -1/6 (pow eps 2))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))>
#<alt (* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (sin eps)>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (cos x))>
#<alt (* eps (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 (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))) 1)))>
#<alt (* -1 x)>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* x (- (/ (sin (+ eps x)) x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))>
#<alt (- (sin x) x)>
#<alt (- (+ (sin x) (* eps (cos x))) x)>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) x)>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (+ eps x)) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (- (sin (- x (* -1 eps))) x)>
#<alt (sin eps)>
#<alt (+ (sin eps) (* x (cos eps)))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))>
#<alt (+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin (- eps (* -1 x)))>
#<alt (sin x)>
#<alt (+ (sin x) (* eps (cos x)))>
#<alt (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))>
#<alt (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (+ eps x))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- x (* -1 eps)))>
#<alt (sin (- 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 (sin eps)>
#<alt (+ (sin eps) (* x (- (cos eps) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))>
#<alt (+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))>
#<alt (* 1/6 (pow x 3))>
#<alt (* (pow x 3) (- 1/6 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))>
#<alt (* 1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))>
#<alt (- (sin x) (+ x (* -1/6 (pow x 3))))>
#<alt (- (+ (sin x) (* eps (cos x))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<alt (- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* -1/6 (pow x 3))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* (pow x 3) (- (/ 1 (pow x 2)) 1/6))>
#<alt (* -1/6 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))>
#<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 (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)>

Calls

63 calls:

Time	Variable		Point	Expression
40.0ms	x	@	-inf	(* x (* x x))
2.0ms	x	@	inf	(* x x)
1.0ms	eps	@	0	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))
1.0ms	x	@	0	(* -1/2 (sin x))
1.0ms	x	@	-inf	(* eps (+ (* eps (* -1/2 (sin x))) (cos x)))

rewrite503.0ms (3.9%)

Memory

37.9MiB live, 464.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 596×	`accelerator-lowering-fma.f32`
6 596×	`accelerator-lowering-fma.f64`
5 130×	`-lowering-.f32`
5 130×	`-lowering-.f64`
4 206×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	72
1	104	72
2	870	72
0	8405	68

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 414

Calls

Call 1

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

Outputs
(+.f64 (.f64 eps (cos.f64 x)) (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(+.f64 (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (.f64 eps (cos.f64 x)))
(-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (.f64 eps (cos.f64 x)))) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (*.f64 eps (cos.f64 x)))))
(fma.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (*.f64 eps (cos.f64 x)))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(fma.f64 (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (.f64 eps eps) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) eps (*.f64 eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))))
(fma.f64 (.f64 eps eps) (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (sin.f64 x) eps) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps (.f64 eps #s(literal -1/2 binary64))) (sin.f64 x) (*.f64 eps (cos.f64 x)))
(/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps eps) (fma.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 eps eps) (neg.f64 (.f64 (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (.f64 eps (cos.f64 x)))))) (+.f64 (pow.f64 (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) #s(literal 3 binary64)) (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (.f64 eps (cos.f64 x))) (-.f64 (.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (.f64 eps eps)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (.f64 (cos.f64 x) (+.f64 (cos.f64 x) (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 x) eps))))) (.f64 eps (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (sin.f64 x) eps) #s(literal 3 binary64)) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
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(/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) (fma.f64 x x (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64) (.f64 #s(literal 1/6 binary64) (.f64 (.f64 x (*.f64 x x)) x)))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (neg.f64 x) x)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64) (.f64 #s(literal 1/6 binary64) (.f64 (.f64 x (.f64 x x)) x)))) (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (*.f64 x x)) x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)))) (fma.f64 x x (.f64 #s(literal -1/36 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (*.f64 x x)) x))))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))))) (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))))) (neg.f64 (fma.f64 x x (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64) (.f64 #s(literal 1/6 binary64) (.f64 (.f64 x (*.f64 x x)) x))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (neg.f64 x) x))) (neg.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x))))
(/.f64 (fma.f64 x x (.f64 #s(literal -1/36 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x) (.f64 x x))) (.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) #s(literal 9 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal 1/46656 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) (fma.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x) (.f64 (neg.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) (.f64 x (.f64 x x))))) (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/46656 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) (.f64 x (.f64 x x))) (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))))))))
(/.f64 (.f64 (-.f64 (.f64 #s(literal 1/46656 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) #s(literal 1/1296 binary64) (fma.f64 (.f64 x x) (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64))))) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))) x)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))) #s(literal 1/1296 binary64)) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64) (.f64 x x)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))))) (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)))))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (neg.f64 x) x)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))) x))))
(/.f64 (neg.f64 (fma.f64 x x (.f64 #s(literal -1/36 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))))) (neg.f64 (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (fma.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))) x))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x))) (.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)))) (+.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64)) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x))) x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)) x)) #s(literal -1 binary64))
(.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))))))))
(.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)) #s(literal 1/36 binary64) (.f64 #s(literal 1/6 binary64) (.f64 (.f64 x (.f64 x x)) x))))))
(.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (neg.f64 x) x)) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x)))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x x)) x))
(.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal -1/216 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 x (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x)))))))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) x) (.f64 (.f64 x x) #s(literal 1/36 binary64)) (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))) x))))
(.f64 (fma.f64 x x (.f64 #s(literal -1/36 binary64) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) x)))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x x))))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify514.0ms (4%)

Memory

9.0MiB live, 887.8MiB allocated

Algorithm

1×	egg-herbie

Rules

20 504×	`accelerator-lowering-fma.f32`
20 504×	`accelerator-lowering-fma.f64`
5 250×	`-lowering-.f32`
5 250×	`-lowering-.f64`
3 986×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	242	1816
1	708	1788
2	1933	1778
3	5119	1708
0	9667	1579

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) (sin x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(cos x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 (* eps (sin x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(* -1/2 (* eps (sin x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(+ (cos x) (* -1/2 (* eps (sin x))))
(* -1/2 x)
(* x (- (* 1/12 (pow x 2)) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (sin x))
(* -1/2 (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)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(sin eps)
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (cos x))
(* eps (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)
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))) 1)))
(* -1 x)
(* x (- (/ (sin (+ eps x)) x) 1))
(* x (- (/ (sin (+ eps x)) x) 1))
(* x (- (/ (sin (+ eps x)) x) 1))
(* -1 x)
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(- (sin x) x)
(- (+ (sin x) (* eps (cos x))) x)
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) x)
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) x)
(- (sin (+ eps x)) x)
(- (sin (+ eps x)) x)
(- (sin (+ eps x)) x)
(- (sin (+ eps x)) x)
(- (sin (- x (* -1 eps))) x)
(- (sin (- x (* -1 eps))) x)
(- (sin (- x (* -1 eps))) x)
(- (sin (- x (* -1 eps))) x)
(sin eps)
(+ (sin eps) (* x (cos eps)))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin (- eps (* -1 x)))
(sin x)
(+ (sin x) (* eps (cos x)))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (+ eps x))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- x (* -1 eps)))
(sin (- 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)))
(sin eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(* 1/6 (pow x 3))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(* 1/6 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(- (sin x) (+ x (* -1/6 (pow x 3))))
(- (+ (sin x) (* eps (cos x))) (+ x (* -1/6 (pow x 3))))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* -1/6 (pow x 3))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* -1/6 (pow x 2))))
(* -1/6 (pow x 3))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(* -1/6 (pow x 3))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(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)
(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)

Outputs
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* -1/2 (* (pow eps 2) (sin x)))
(.f64 (sin.f64 x) (.f64 eps (*.f64 eps #s(literal -1/2 binary64))))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* (pow eps 2) (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(fma.f64 x (.f64 eps (.f64 eps #s(literal -1/2 binary64))) eps)
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x))) eps)
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/12 (* (pow eps 2) x)))))))
(fma.f64 x (fma.f64 eps (.f64 #s(literal -1/2 binary64) (+.f64 eps x)) (.f64 x (.f64 (.f64 eps (*.f64 eps x)) #s(literal 1/12 binary64)))) eps)
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(* eps (+ (cos x) (* -1/2 (* eps (sin x)))))
(.f64 eps (fma.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x)))
(cos x)
(cos.f64 x)
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* eps (+ (* -1/2 (sin x)) (/ (cos x) eps)))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* -1/2 (* eps (sin x)))
(.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 (sin x)))))
(-.f64 (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x))) (neg.f64 (cos.f64 x)))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (* eps x)))
(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) (+.f64 eps x) #s(literal 1 binary64))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/12 (* eps x)) 1/2)))))
(fma.f64 x (fma.f64 x (fma.f64 eps (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) #s(literal 1 binary64))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(+ (cos x) (* -1/2 (* eps (sin x))))
(fma.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)) (cos.f64 x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* x (- (* 1/12 (pow x 2)) 1/2))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* -1/240 (pow x 2)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* x (- (* (pow x 2) (+ 1/12 (* (pow x 2) (- (* 1/10080 (pow x 2)) 1/240)))) 1/2))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/10080 binary64)) #s(literal -1/240 binary64)) #s(literal 1/12 binary64)) #s(literal -1/2 binary64)))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
(* -1/2 (sin x))
(*.f64 #s(literal -1/2 binary64) (sin.f64 x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 (.f64 x 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)
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 eps (.f64 eps #s(literal -1/6 binary64))) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (fma.f64 (.f64 eps eps) #s(literal 1/120 binary64) #s(literal -1/6 binary64)) (.f64 eps (*.f64 eps eps)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/5040 binary64) #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 eps (.f64 eps eps)) eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(sin eps)
(sin.f64 eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* (pow x 2) (+ (* -1/720 (* eps (pow x 2))) (* 1/24 eps))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 eps (fma.f64 (.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64))) (*.f64 eps #s(literal -1/2 binary64))) eps)
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (cos.f64 x))
(* eps (cos x))
(*.f64 eps (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 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 (*.f64 x x) #s(literal -1/720 binary64) #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (fma.f64 x (cos.f64 eps) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps)))))) 1)))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (fma.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps) #s(literal -1 binary64))) (sin.f64 eps))
(* -1 x)
(neg.f64 x)
(* x (- (/ (sin (+ eps x)) x) 1))
(-.f64 (sin.f64 (+.f64 eps x)) x)
(* x (- (/ (sin (+ eps x)) x) 1))
(-.f64 (sin.f64 (+.f64 eps x)) x)
(* x (- (/ (sin (+ eps x)) x) 1))
(-.f64 (sin.f64 (+.f64 eps x)) x)
(* -1 x)
(neg.f64 x)
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(-.f64 (sin.f64 (+.f64 eps x)) x)
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(-.f64 (sin.f64 (+.f64 eps x)) x)
(* -1 (* x (+ 1 (* -1 (/ (sin (- eps (* -1 x))) x)))))
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin x) x)
(-.f64 (sin.f64 x) x)
(- (+ (sin x) (* eps (cos x))) x)
(-.f64 (fma.f64 eps (cos.f64 x) (sin.f64 x)) x)
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) x)
(-.f64 (fma.f64 eps (cos.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x))) x)
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) x)
(fma.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (-.f64 (sin.f64 x) x))
(- (sin (+ eps x)) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (+ eps x)) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (+ eps x)) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (+ eps x)) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(- (sin (- x (* -1 eps))) x)
(-.f64 (sin.f64 (+.f64 eps x)) x)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (cos eps)))
(fma.f64 x (cos.f64 eps) (sin.f64 eps))
(+ (sin eps) (* x (+ (cos eps) (* -1/2 (* x (sin eps))))))
(fma.f64 x (cos.f64 eps) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps)))
(+ (sin eps) (* x (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* -1/6 (* x (cos eps))))))))
(fma.f64 x (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) (.f64 (fma.f64 x (*.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps))) (sin.f64 eps))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin (- eps (* -1 x)))
(sin.f64 (+.f64 eps x))
(sin x)
(sin.f64 x)
(+ (sin x) (* eps (cos x)))
(fma.f64 eps (cos.f64 x) (sin.f64 x))
(+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x))))))
(fma.f64 eps (cos.f64 x) (.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x)))
(+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x))))))))
(fma.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (*.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (sin.f64 x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (+ eps x))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.f64 (+.f64 eps x))
(sin (- x (* -1 eps)))
(sin.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)
(sin eps)
(sin.f64 eps)
(+ (sin eps) (* x (- (cos eps) 1)))
(fma.f64 x (+.f64 #s(literal -1 binary64) (cos.f64 eps)) (sin.f64 eps))
(+ (sin eps) (* x (- (+ (cos eps) (* -1/2 (* x (sin eps)))) 1)))
(+.f64 (fma.f64 x (cos.f64 eps) (.f64 (fma.f64 x (.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 eps))) (neg.f64 x))
(+ (sin eps) (* x (- (+ (cos eps) (* x (+ (* -1/2 (sin eps)) (* x (+ 1/6 (* -1/6 (cos eps))))))) 1)))
(fma.f64 x (+.f64 (fma.f64 x (.f64 #s(literal -1/2 binary64) (sin.f64 eps)) #s(literal -1 binary64)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 eps)))) (sin.f64 eps))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* (pow x 3) (- 1/6 (/ 1 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (.f64 x (*.f64 x x))))))))
(* (pow x 3) (- (+ 1/6 (/ (sin (+ eps x)) (pow x 3))) (/ 1 (pow x 2))))
(.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (.f64 x (*.f64 x x))))))))
(* 1/6 (pow x 3))
(.f64 #s(literal 1/6 binary64) (.f64 x (*.f64 x x)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/6)))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (.f64 x (*.f64 x x))))))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (sin (- eps (* -1 x))) (pow x 3))) (/ 1 (pow x 2))) 1/6)))
(.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (/.f64 (sin.f64 (+.f64 eps x)) (neg.f64 (.f64 x (*.f64 x x))))))))
(- (sin x) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x))
(- (+ (sin x) (* eps (cos x))) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (fma.f64 eps (cos.f64 x) (sin.f64 x)))
(- (+ (sin x) (* eps (+ (cos x) (* -1/2 (* eps (sin x)))))) (+ x (* -1/6 (pow x 3))))
(fma.f64 eps (cos.f64 x) (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/2 binary64)) #s(literal 1 binary64)) (sin.f64 x) (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)))))
(- (+ (sin x) (* eps (+ (cos x) (* eps (+ (* -1/2 (sin x)) (* -1/6 (* eps (cos x)))))))) (+ x (* -1/6 (pow x 3))))
(fma.f64 eps (fma.f64 (fma.f64 eps (.f64 eps #s(literal -1/6 binary64)) #s(literal 1 binary64)) (cos.f64 x) (.f64 eps (.f64 #s(literal -1/2 binary64) (sin.f64 x)))) (fma.f64 x (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 x)))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(- (sin (+ eps x)) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
(- (sin (- x (* -1 eps))) (+ x (* -1/6 (pow x 3))))
(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* -1/6 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/6 binary64)))
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* (pow x 3) (- (/ 1 (pow x 2)) 1/6))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* -1/6 (pow x 3))
(.f64 x (.f64 (*.f64 x x) #s(literal -1/6 binary64)))
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* -1 (* (pow x 3) (- 1/6 (/ 1 (pow x 2)))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval92.0ms (0.7%)

Memory: -23.1MiB live, 207.7MiB allocated
Compiler: Compiled 22 969 to 1 544 computations (93.3% saved)

prune71.0ms (0.6%)

Memory

18.7MiB live, 139.8MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	778	6	784
Fresh	0	0	0
Picked	5	0	5
Done	0	0	0
Total	783	6	789

Accuracy

100.0%

Counts

789 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
	60.2%	(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
▶	99.7%	(fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x))) eps)
▶	99.7%	(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
▶	100.0%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))
▶	98.8%	eps

Compiler

Compiled 130 to 80 computations (38.5% saved)

simplify32.0ms (0.3%)

Memory

19.4MiB live, 57.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(.f64 eps (.f64 x x))
✓	cost-diff	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
✓	cost-diff	(+.f64 eps x)
✓	cost-diff	(*.f64 eps (+.f64 eps x))
✓	cost-diff	(.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x)))
✓	cost-diff	(fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x))) eps)
✓	cost-diff	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) (cos.f64 x))
✓	cost-diff	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))

Rules

904×	`accelerator-lowering-fma.f32`
904×	`accelerator-lowering-fma.f64`
650×	`-lowering-.f32`
650×	`-lowering-.f64`
378×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	113
1	69	113
2	198	113
3	395	113
4	489	113
5	500	113
6	665	113
7	665	113
8	666	113
0	666	106

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* eps (+ (* eps (* x -1/2)) (cos x)))
eps
(+ (* eps (* x -1/2)) (cos x))
(* x -1/2)
x
-1/2
(cos x)
eps
(+ (* eps (* x (* x -1/2))) eps)
eps
(* x (* x -1/2))
x
(* x -1/2)
-1/2
(+ (* x (* -1/2 (* eps (+ eps x)))) eps)
x
(* -1/2 (* eps (+ eps x)))
-1/2
(* eps (+ eps x))
eps
(+ eps x)
(+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)
(* eps (* x x))
eps
(* x x)
x
(+ (* x (* x 1/24)) -1/2)
(* x 1/24)
1/24
-1/2

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

localize83.0ms (0.6%)

Memory

-17.5MiB live, 158.9MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 eps (.f64 x x))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	100.0%	(fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x))) eps)
✓	accuracy	100.0%	(+.f64 eps x)
✓	accuracy	100.0%	(.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x)))
✓	accuracy	99.8%	(*.f64 eps (+.f64 eps x))
✓	accuracy	100.0%	(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
✓	accuracy	100.0%	(.f64 x (.f64 x #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) (cos.f64 x))
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	100.0%	(.f64 eps (fma.f64 eps (.f64 x #s(literal -1/2 binary64)) (cos.f64 x)))

Samples

48.0ms

256×

valid

Compiler

Compiled 108 to 26 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 20.0ms (62.4% of total)

ival-add: 6.0ms (18.7% of total)

const: 4.0ms (12.5% of total)

ival-cos: 2.0ms (6.2% of total)

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

exact: 0.0ms (0% of total)

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

series24.0ms (0.2%)

Memory

-11.7MiB live, 29.9MiB allocated

Counts

15 → 288

Calls

Call 1

Inputs
#<alt (* eps (+ (* eps (* x -1/2)) (cos x)))>
#<alt (+ (* eps (* x -1/2)) (cos x))>
#<alt (* x -1/2)>
#<alt (cos x)>
#<alt (+ (* eps (* x (* x -1/2))) eps)>
#<alt (* x (* x -1/2))>
#<alt (+ (* x (* -1/2 (* eps (+ eps x)))) eps)>
#<alt (* -1/2 (* eps (+ eps x)))>
#<alt (* eps (+ eps x))>
#<alt (+ eps x)>
#<alt (+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)>
#<alt (* eps (* x x))>
#<alt (* x x)>
#<alt (+ (* x (* x 1/24)) -1/2)>
#<alt (* x 1/24)>

Outputs
#<alt (* eps (cos x))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* eps (+ (cos x) (* -1/2 (* eps x))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt (* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))>
#<alt (cos x)>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (+ (cos x) (* -1/2 (* eps x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* eps (+ (* -1/2 x) (/ (cos x) eps)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt (* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))>
#<alt 1>
#<alt (+ 1 (* -1/2 (* eps x)))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))>
#<alt (+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/24 (pow x 2)) 1/2)))))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* x (+ (* -1/2 eps) (/ (cos x) x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt 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 (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt (* -1 (* eps (- (* 1/2 (pow x 2)) 1)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt (* -1/2 (pow x 2))>
#<alt eps>
#<alt (+ eps (* -1/2 (* (pow eps 2) x)))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))>
#<alt (* -1/2 (* eps (pow x 2)))>
#<alt (* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))>
#<alt (* eps (+ 1 (* -1/2 (pow x 2))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))>
#<alt (* -1/2 (* (pow eps 2) x))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))>
#<alt (* -1/2 (* eps x))>
#<alt (* eps (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* eps (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* eps (+ (* -1/2 eps) (* -1/2 x)))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))>
#<alt (* -1/2 (pow eps 2))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))>
#<alt (* -1/2 (* eps x))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))>
#<alt (* -1/2 (* eps x))>
#<alt (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))>
#<alt (* eps x)>
#<alt (* eps (+ eps x))>
#<alt (* eps (+ eps x))>
#<alt (* eps (+ eps x))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (* (pow eps 2) (+ 1 (/ x eps)))>
#<alt (pow eps 2)>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (+ (* eps x) (pow eps 2))>
#<alt (* eps x)>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* x (+ eps (/ (pow eps 2) x)))>
#<alt (* eps x)>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<alt (* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))>
#<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 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 (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))>
#<alt (* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))>
#<alt eps>
#<alt (+ eps (* -1/2 (* eps (pow x 2))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))>
#<alt (* 1/24 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))>
#<alt (* 1/24 (* eps (pow x 4)))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))>
#<alt (* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (pow x 2))>
#<alt (* eps (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 -1/2>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (- (* 1/24 (pow x 2)) 1/2)>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>

Calls

72 calls:

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

rewrite376.0ms (2.9%)

Memory

29.3MiB live, 452.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

9 206×	`accelerator-lowering-fma.f32`
9 206×	`accelerator-lowering-fma.f64`
5 506×	`-lowering-.f32`
5 506×	`-lowering-.f64`
3 716×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	96
1	137	96
2	1137	96
0	8427	89

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 464

Calls

Call 1

Inputs
(* eps (+ (* eps (* x -1/2)) (cos x)))
(+ (* eps (* x -1/2)) (cos x))
(* x -1/2)
(cos x)
(+ (* eps (* x (* x -1/2))) eps)
(* x (* x -1/2))
(+ (* x (* -1/2 (* eps (+ eps x)))) eps)
(* -1/2 (* eps (+ eps x)))
(* eps (+ eps x))
(+ eps x)
(+ (* (* eps (* x x)) (+ (* x (* x 1/24)) -1/2)) eps)
(* eps (* x x))
(* x x)
(+ (* x (* x 1/24)) -1/2)
(* x 1/24)

Outputs
(+.f64 (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))) (.f64 eps (cos.f64 x)))
(+.f64 (.f64 eps (cos.f64 x)) (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps)))) (-.f64 (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))) (.f64 eps (cos.f64 x)))) (/.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (-.f64 (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (cos.f64 x)))))
(fma.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64))) (*.f64 eps (cos.f64 x)))
(fma.f64 eps (cos.f64 x) (.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(fma.f64 (.f64 x #s(literal -1/2 binary64)) (.f64 eps eps) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) eps (*.f64 eps (cos.f64 x)))
(fma.f64 (cos.f64 x) eps (.f64 eps (.f64 eps (*.f64 x #s(literal -1/2 binary64)))))
(fma.f64 (.f64 eps eps) (.f64 x #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps x) (.f64 eps #s(literal -1/2 binary64)) (*.f64 eps (cos.f64 x)))
(fma.f64 (.f64 eps (.f64 eps x)) #s(literal -1/2 binary64) (*.f64 eps (cos.f64 x)))
(/.f64 eps (/.f64 #s(literal 1 binary64) (fma.f64 eps (*.f64 x #s(literal -1/2 binary64)) (cos.f64 x))))
(/.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (pow.f64 (.f64 eps (cos.f64 x)) #s(literal 3 binary64))) (fma.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps))) (fma.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 (.f64 (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (cos.f64 x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps))) (fma.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 (.f64 (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))) (.f64 eps (cos.f64 x)))))) (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x)))) (pow.f64 (*.f64 eps (cos.f64 x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))) (.f64 eps (cos.f64 x))) (-.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps)))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (.f64 (.f64 eps x) #s(literal 1/2 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps)))) (.f64 eps (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (cos.f64 x)) (.f64 eps (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 x) (+.f64 (cos.f64 x) (.f64 (.f64 eps x) #s(literal 1/2 binary64))) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps)))) (.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 (.f64 eps (.f64 eps eps)) (.f64 x (.f64 x x))) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 eps (.f64 x #s(literal -1/2 binary64))) (cos.f64 x)) (.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) eps)))
(/.f64 (-.f64 (.f64 (.f64 eps eps) (.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 eps eps)))) (.f64 (.f64 eps eps) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))) (-.f64 (.f64 eps (.f64 eps (.f64 x #s(literal -1/2 binary64)))) (*.f64 eps (cos.f64 x))))
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(*.f64 x #s(literal 1/24 binary64))
(*.f64 #s(literal 1/24 binary64) x)

simplify336.0ms (2.6%)

Memory

-25.6MiB live, 453.3MiB allocated

Algorithm

1×	egg-herbie

Rules

15 228×	`accelerator-lowering-fma.f32`
15 228×	`accelerator-lowering-fma.f64`
3 716×	`-lowering-.f32`
3 716×	`-lowering-.f64`
2 306×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	171	2030
1	564	2016
2	1538	2002
3	3183	1980
4	6401	1980
0	8361	1849

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

Inputs
(* eps (cos x))
(* eps (+ (cos x) (* -1/2 (* eps x))))
(* eps (+ (cos x) (* -1/2 (* eps x))))
(* eps (+ (cos x) (* -1/2 (* eps x))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
(* (pow eps 2) (+ (* -1/2 x) (/ (cos x) eps)))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (pow eps 2)) (* x (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))))
(* -1/2 (* (pow eps 2) x))
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))
(* x (+ (* -1/2 (pow eps 2)) (/ (* eps (cos x)) x)))
(* -1/2 (* (pow eps 2) x))
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))
(* -1 (* x (+ (* -1 (/ (* eps (cos x)) x)) (* 1/2 (pow eps 2)))))
(cos x)
(+ (cos x) (* -1/2 (* eps x)))
(+ (cos x) (* -1/2 (* eps x)))
(+ (cos x) (* -1/2 (* eps x)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 x) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (/ (cos x) eps)))
(* eps (+ (* -1/2 x) (/ (cos x) eps)))
(* -1/2 (* eps x))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))
(* -1 (* eps (+ (* -1 (/ (cos x) eps)) (* 1/2 x))))
1
(+ 1 (* -1/2 (* eps x)))
(+ 1 (* x (+ (* -1/2 eps) (* -1/2 x))))
(+ 1 (* x (+ (* -1/2 eps) (* x (- (* 1/24 (pow x 2)) 1/2)))))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (/ (cos x) x)))
(* x (+ (* -1/2 eps) (/ (cos x) x)))
(* x (+ (* -1/2 eps) (/ (cos x) x)))
(* -1/2 (* eps x))
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))
(* -1 (* x (+ (* -1 (/ (cos x) x)) (* 1/2 eps))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
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 (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
(* -1 (* eps (- (* 1/2 (pow x 2)) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* -1/2 (* eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* (pow x 2) (+ (* -1/2 eps) (/ eps (pow x 2))))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
(* -1/2 (pow x 2))
eps
(+ eps (* -1/2 (* (pow eps 2) x)))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(+ eps (* x (+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* (pow x 2) (+ (* -1/2 eps) (+ (* -1/2 (/ (pow eps 2) x)) (/ eps (pow x 2)))))
(* -1/2 (* eps (pow x 2)))
(* (pow x 2) (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* (pow x 2) (+ (* -1 (/ (+ (* -1 (/ eps x)) (* 1/2 (pow eps 2))) x)) (* -1/2 eps)))
(* eps (+ 1 (* -1/2 (pow x 2))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* eps (+ 1 (+ (* -1/2 (* eps x)) (* -1/2 (pow x 2)))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* (pow eps 2) (+ (* -1/2 x) (+ (* -1/2 (/ (pow x 2) eps)) (/ 1 eps))))
(* -1/2 (* (pow eps 2) x))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* (pow eps 2) (+ (* -1 (/ (- (* 1/2 (pow x 2)) 1) eps)) (* -1/2 x)))
(* -1/2 (* eps x))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* eps (+ (* -1/2 eps) (* -1/2 x)))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* (pow eps 2) (- (* -1/2 (/ x eps)) 1/2))
(* -1/2 (pow eps 2))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(+ (* -1/2 (* eps x)) (* -1/2 (pow eps 2)))
(* -1/2 (* eps x))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* x (+ (* -1/2 eps) (* -1/2 (/ (pow eps 2) x))))
(* -1/2 (* eps x))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* 1/2 eps) (* 1/2 (/ (pow eps 2) x)))))
(* eps x)
(* eps (+ eps x))
(* eps (+ eps x))
(* eps (+ eps x))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(pow eps 2)
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(* (pow eps 2) (+ 1 (/ x eps)))
(pow eps 2)
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(+ (* eps x) (pow eps 2))
(* eps x)
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* x (+ eps (/ (pow eps 2) x)))
(* eps x)
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
(* -1 (* x (+ (* -1 eps) (* -1 (/ (pow eps 2) x)))))
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)))
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)))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* eps (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
(* -1 (* eps (- (* -1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) 1)))
eps
(+ eps (* -1/2 (* eps (pow x 2))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(+ eps (* (pow x 2) (+ (* -1/2 eps) (* 1/24 (* eps (pow x 2))))))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* 1/24 (* eps (pow x 4)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (* 1/24 eps)))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* (pow x 4) (+ (* -1/2 (/ eps (pow x 2))) (+ (* 1/24 eps) (/ eps (pow x 4)))))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (pow x 2))
(* eps (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)
-1/2
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(- (* 1/24 (pow x 2)) 1/2)
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)

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

eval115.0ms (0.9%)

Memory: 2.7MiB live, 115.6MiB allocated
Compiler: Compiled 19 424 to 1 608 computations (91.7% saved)

prune65.0ms (0.5%)

Memory

19.3MiB live, 108.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	765	1	766
Fresh	0	1	1
Picked	1	4	5
Done	0	0	0
Total	766	6	772

Accuracy

100.0%

Counts

772 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
▶	60.2%	(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
✓	99.7%	(fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x))) eps)
▶	100.0%	(fma.f64 eps (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))))) eps)
✓	99.7%	(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
✓	98.8%	eps

Compiler

Compiled 72 to 43 computations (40.3% saved)

simplify579.0ms (4.5%)

Memory

17.6MiB live, 520.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Program
✓	cost-diff	(sin.f64 (+.f64 eps x))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
✓	cost-diff	(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
✓	cost-diff	(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))))
✓	cost-diff	(.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))
✓	cost-diff	(fma.f64 eps (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))))) eps)

Rules

24 824×	`accelerator-lowering-fma.f32`
24 824×	`accelerator-lowering-fma.f64`
3 260×	`-lowering-.f32`
3 260×	`-lowering-.f64`
2 472×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	105
1	58	105
2	159	97
3	341	97
4	708	97
5	931	97
6	1219	97
7	1417	97
8	1778	97
9	2327	97
10	4394	97
11	6036	97
12	6855	97
13	6968	97
14	6973	97
15	6974	97
16	7111	97
17	7379	97
18	7381	97
19	7381	97
20	7381	97
0	8092	89

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize85.0ms (0.7%)

Memory

-12.4MiB live, 124.1MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 eps x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(sin.f64 (+.f64 eps x))
✓	accuracy	60.5%	(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)))
✓	accuracy	99.9%	(fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64))))
✓	accuracy	99.7%	(.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64)))))

Samples

29.0ms	158×	0	valid
28.0ms	94×	1	valid
2.0ms	3×	3	valid
1.0ms	1×	2	valid

Compiler

Compiled 95 to 23 computations (75.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 14.0ms (36.9% of total)

ival-add: 9.0ms (23.7% of total)

const: 6.0ms (15.8% of total)

adjust: 4.0ms (10.5% of total)

ival-sin: 4.0ms (10.5% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.1%)

Memory

-18.8MiB live, 20.2MiB allocated

Counts

9 → 180

Calls

Call 1

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

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

Calls

45 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(* x (+ (* 1/24 (* x x)) -1/2))
1.0ms	eps	@	0	(+ (* eps (* x (+ (* eps -1/2) (* x (+ (* 1/24 (* x x)) -1/2))))) eps)
1.0ms	eps	@	inf	(+ (* eps (* x (+ (* eps -1/2) (* x (+ (* 1/24 (* x x)) -1/2))))) eps)
1.0ms	eps	@	-inf	(+ (* eps (* x (+ (* eps -1/2) (* x (+ (* 1/24 (* x x)) -1/2))))) eps)
0.0ms	eps	@	inf	(+ (* x (+ (* (* x x) 1/6) -1)) (sin (+ eps x)))

rewrite336.0ms (2.6%)

Memory

16.3MiB live, 514.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 096×	`-lowering-.f32`
5 096×	`-lowering-.f64`
4 246×	`/-lowering-/.f32`
4 246×	`/-lowering-/.f64`
4 148×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	87
1	139	86
2	1199	85
0	8324	76

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 378

Calls

Call 1

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

Outputs
(+.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)))
(+.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps)
(+.f64 (/.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps)) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps))))
(-.f64 (/.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps)) (/.f64 (.f64 eps eps) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps)))
(-.f64 (/.f64 (.f64 eps eps) (-.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)))) (/.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (-.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)))))
(fma.f64 eps (.f64 x (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) eps)
(fma.f64 x (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) eps) eps)
(fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x) eps)
(fma.f64 (.f64 x (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) eps eps)
(fma.f64 (.f64 eps x) (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64))) eps)
(fma.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps)) (neg.f64 (/.f64 (.f64 eps eps) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps))))
(fma.f64 (.f64 eps (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (*.f64 eps #s(literal -1/2 binary64)))) x eps)
(fma.f64 (.f64 (.f64 eps x) (fma.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (-.f64 (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))) (.f64 eps #s(literal -1/2 binary64))) (.f64 (*.f64 eps eps) #s(literal 1/4 binary64)))) eps)
(fma.f64 (.f64 (.f64 eps x) (-.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x (.f64 (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64))))) eps)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x) eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x) eps)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 eps eps (-.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))))) (fma.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (*.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (-.f64 (.f64 eps eps) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))))))
(/.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (.f64 eps eps))) (fma.f64 eps (-.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)))))
(/.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (.f64 eps eps))) (fma.f64 eps eps (-.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x))))))
(/.f64 (.f64 (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x) eps) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps)) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 eps (-.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))))))
(/.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (.f64 eps eps)))) (neg.f64 (fma.f64 eps eps (-.f64 (.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x))) (.f64 eps (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (*.f64 eps x)))))))
(/.f64 (neg.f64 (.f64 (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x) eps) (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps))) (neg.f64 (-.f64 (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) (.f64 eps #s(literal -1/2 binary64))) (.f64 eps x)) eps)))
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(.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x (-.f64 x eps) (*.f64 eps eps))))
(.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 (.f64 eps eps) (.f64 eps x)))))
(.f64 (.f64 (+.f64 eps x) (-.f64 eps x)) (/.f64 #s(literal 1 binary64) (-.f64 eps x)))
(.f64 (neg.f64 (fma.f64 eps (.f64 eps eps) (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (-.f64 x eps) (*.f64 eps eps)))))
(.f64 (neg.f64 (.f64 (+.f64 eps x) (-.f64 eps x))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 eps x))))
(.f64 (-.f64 (.f64 x x) (*.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 x eps)))

simplify424.0ms (3.3%)

Memory

-9.2MiB live, 447.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 570×	`accelerator-lowering-fma.f32`
12 570×	`accelerator-lowering-fma.f64`
4 756×	`-lowering-.f32`
4 756×	`-lowering-.f64`
2 404×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	214	1786
1	635	1744
2	1816	1640
3	5481	1624
0	8323	1518

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

eval139.0ms (1.1%)

Memory: -0.0MiB live, 115.9MiB allocated
Compiler: Compiled 20 547 to 1 609 computations (92.2% saved)

prune159.0ms (1.2%)

Memory

-11.3MiB live, 104.2MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	578	0	578
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	578	6	584

Accuracy

100.0%

Counts

584 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (.f64 eps (.f64 x x)) (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal -1/2 binary64)) eps)
✓	60.2%	(fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1 binary64)) (sin.f64 (+.f64 eps x)))
✓	99.7%	(fma.f64 x (.f64 #s(literal -1/2 binary64) (.f64 eps (+.f64 eps x))) eps)
✓	100.0%	(fma.f64 eps (.f64 x (fma.f64 eps #s(literal -1/2 binary64) (.f64 x (fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal -1/2 binary64))))) eps)
✓	99.7%	(fma.f64 eps (.f64 x (.f64 x #s(literal -1/2 binary64))) eps)
✓	98.8%	eps

Compiler

Compiled 185 to 86 computations (53.5% saved)

regimes12.0ms (0.1%)

Memory

23.3MiB live, 23.3MiB allocated

Counts

13 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	x
4.0ms	eps

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes6.0ms (0%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes39.0ms (0.3%)

Memory

-39.9MiB live, 14.6MiB allocated

Counts

3 → 1

Calls

Call 1

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

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

Calls

3 calls:

35.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.0ms	eps
2.0ms	x

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes5.0ms (0%)

Memory

10.3MiB live, 10.3MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

regimes4.0ms (0%)

Memory

9.2MiB live, 9.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
eps

Outputs
eps

Calls

3 calls:

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

Results

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

simplify36.0ms (0.3%)

Memory

-26.2MiB live, 13.5MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	30	48

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness866.0ms (6.8%)

Memory

11.6MiB live, 486.3MiB allocated

Rules

20 504×	`accelerator-lowering-fma.f32`
20 504×	`accelerator-lowering-fma.f64`
16 678×	`accelerator-lowering-fma.f32`
16 678×	`accelerator-lowering-fma.f64`
15 228×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	171	2030
1	564	2016
2	1538	2002
3	3183	1980
4	6401	1980
0	8361	1849
0	107	496
1	314	496
2	775	489
3	2836	489
4	6173	489
0	8126	458
0	242	1816
1	708	1788
2	1933	1778
3	5119	1708
0	9667	1579

Stop Event

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

Compiler

Compiled 138 to 79 computations (42.8% saved)

preprocess122.0ms (1%)

Memory: -11.2MiB live, 149.6MiB allocated
Compiler: Compiled 212 to 120 computations (43.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
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	24	113
1	69	113
2	198	113
3	395	113
4	489	113
5	500	113
6	665	113
7	665	113
8	666	113
0	666	106

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
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	24	113
1	69	113
2	198	113
3	395	113
4	489	113
5	500	113
6	665	113
7	665	113
8	666	113
0	666	106

analyze46.0ms (0.4%)

sample6.2s (48.5%)

preprocess25.0ms (0.2%)

explain97.0ms (0.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify8.0ms (0.1%)

localize28.0ms (0.2%)

series11.0ms (0.1%)

rewrite344.0ms (2.7%)

simplify527.0ms (4.1%)

eval54.0ms (0.4%)

prune78.0ms (0.6%)

simplify135.0ms (1.1%)

localize131.0ms (1%)

series56.0ms (0.4%)

rewrite503.0ms (3.9%)

simplify514.0ms (4%)

eval92.0ms (0.7%)

prune71.0ms (0.6%)

simplify32.0ms (0.3%)

localize83.0ms (0.6%)

series24.0ms (0.2%)

rewrite376.0ms (2.9%)

simplify336.0ms (2.6%)

eval115.0ms (0.9%)

prune65.0ms (0.5%)

simplify579.0ms (4.5%)

localize85.0ms (0.7%)

series14.0ms (0.1%)

rewrite336.0ms (2.6%)

simplify424.0ms (3.3%)

eval139.0ms (1.1%)

prune159.0ms (1.2%)

regimes12.0ms (0.1%)

regimes6.0ms (0%)

regimes39.0ms (0.3%)

regimes5.0ms (0%)

regimes4.0ms (0%)

simplify36.0ms (0.3%)

soundness866.0ms (6.8%)

preprocess122.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	18	39
1	38	35
2	86	35
3	169	35
4	310	35
5	367	35
6	445	35
7	482	35
8	491	35
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	24	113
1	69	113
2	198	113
3	395	113
4	489	113
5	500	113
6	665	113
7	665	113
8	666	113
0	666	106