Metrics for sintan (problem 3.4.5)

analyze369.0ms (2%)

Memory

39.7MiB live, 426.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	49.9%	50.1%	0%	0%	0%	0
0%	0%	49.9%	50.1%	0%	0%	0%	1
0%	0%	49.9%	50.1%	0%	0%	0%	2
0%	0%	49.9%	50.1%	0%	0%	0%	3
0%	0%	49.9%	50.1%	0%	0%	0%	4
0%	0%	49.9%	50.1%	0%	0%	0%	5
0%	0%	49.9%	50.1%	0%	0%	0%	6
0%	0%	49.9%	50.1%	0%	0%	0%	7
0%	0%	49.9%	50.1%	0%	0%	0%	8
0%	0%	49.9%	50.1%	0%	0%	0%	9
0%	0%	49.9%	50.1%	0%	0%	0%	10
0%	0%	49.9%	50.1%	0%	0%	0%	11
0%	0%	49.9%	50.1%	0%	0%	0%	12

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample9.4s (50.5%)

Memory

57.6MiB live, 10 308.0MiB allocated

Samples

6.5s	4 499×	2	valid
1.6s	1 175×	3	valid
739.0ms	2 472×	1	valid
10.0ms	110×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 8.5s

ival-tan: 4.7s (55.1% of total)

ival-sin: 2.7s (31.3% of total)

adjust: 319.0ms (3.7% of total)

const: 313.0ms (3.7% of total)

ival-sub: 297.0ms (3.5% of total)

ival-div: 108.0ms (1.3% of total)

ival-<=: 102.0ms (1.2% of total)

ival-and: 12.0ms (0.1% of total)

ival-assert: 3.0ms (0% of total)

Bogosity

preprocess57.0ms (0.3%)

Memory

10.1MiB live, 47.2MiB allocated

Algorithm

1×	egg-herbie

Rules

320×	`lower-fma.f64`
320×	`lower-fma.f32`
192×	`lower-*.f64`
192×	`lower-*.f32`
144×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Outputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Symmetry

(abs eps)

explain568.0ms (3.1%)

Memory

-15.8MiB live, 848.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
160	0	-	-	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`
95	0	-	-	`(-.f64 eps (tan.f64 eps))`
94	1	(6.382894325532866e-108)	-	`(-.f64 eps (sin.f64 eps))`
0	0	-	-	`(tan.f64 eps)`
0	0	-	-	`eps`
0	0	-	-	`(sin.f64 eps)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`	u/u	160	0
↳	`(-.f64 eps (sin.f64 eps))`	underflow	160
↳	`(-.f64 eps (tan.f64 eps))`	underflow	160
`-.f64`	`(-.f64 eps (sin.f64 eps))`	cancellation	95	1
`-.f64`	`(-.f64 eps (tan.f64 eps))`	cancellation	95	0

Confusion

	Predicted +	Predicted -
+	255	0
-	0	1

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	255	0	0
-	0	1	0

Precision?

0.99609375

Recall?

1.0

Freqs

test

number	freq
0	1
1	160
2	95

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

371.0ms	270×	2	valid
60.0ms	62×	3	valid
29.0ms	172×	1	valid
1.0ms	8×	0	valid

Compiler

Compiled 68 to 28 computations (58.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 434.0ms

ival-tan: 255.0ms (58.8% of total)

ival-sin: 140.0ms (32.3% of total)

adjust: 16.0ms (3.7% of total)

ival-sub: 15.0ms (3.5% of total)

ival-div: 6.0ms (1.4% of total)

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

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.6MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	1.6%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify26.0ms (0.1%)

Memory

5.4MiB live, 44.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(-.f64 eps (tan.f64 eps))
✓	cost-diff	(sin.f64 eps)
✓	cost-diff	(-.f64 eps (sin.f64 eps))
✓	cost-diff	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Rules

320×	`lower-fma.f64`
320×	`lower-fma.f32`
192×	`lower-*.f64`
192×	`lower-*.f32`
144×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
eps
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

Outputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
eps
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

localize318.0ms (1.7%)

Memory

14.7MiB live, 549.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 eps)
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	66.7%	(-.f64 eps (sin.f64 eps))
✓	accuracy	37.9%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Samples

270.0ms	135×	2	valid
22.0ms	31×	3	valid
15.0ms	86×	1	valid
0.0ms	4×	0	valid

Compiler

Compiled 24 to 8 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 287.0ms

ival-tan: 203.0ms (70.8% of total)

ival-sin: 64.0ms (22.3% of total)

adjust: 8.0ms (2.8% of total)

ival-sub: 8.0ms (2.8% of total)

ival-div: 3.0ms (1% of total)

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

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

series5.0ms (0%)

Memory

14.0MiB live, 14.0MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))>
#<alt (-.f64 eps (sin.f64 eps))>
#<alt (sin.f64 eps)>
#<alt (-.f64 eps (tan.f64 eps))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<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 (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	eps	@	inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	-inf	(/ (- eps (sin eps)) (- eps (tan eps)))
1.0ms	eps	@	0	(/ (- eps (sin eps)) (- eps (tan eps)))
0.0ms	eps	@	inf	(- eps (tan eps))
0.0ms	eps	@	-inf	(- eps (tan eps))

rewrite329.0ms (1.8%)

Memory

-26.8MiB live, 540.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 318×	`lower-*.f64`
4 318×	`lower-*.f32`
3 264×	`lower-/.f32`
3 262×	`lower-/.f64`
2 758×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
0	11	19
1	51	19
2	408	19
3	5947	19
0	8258	19

Stop Event

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

Counts

4 → 419

Calls

Call 1

Inputs
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(-.f64 eps (sin.f64 eps))
(sin.f64 eps)
(-.f64 eps (tan.f64 eps))

Outputs
(exp.f64 (*.f64 (log.f64 (/.f64 (-.f64 eps (tan.f64 eps)) (-.f64 eps (sin.f64 eps)))) #s(literal -1 binary64)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps))))
(+.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (sin.f64 eps))))
(+.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (neg.f64 (sin.f64 eps))) (/.f64 eps (-.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (.f64 eps eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (*.f64 eps (tan.f64 eps))))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)))
(+.f64 (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (tan.f64 eps)) (.f64 (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) eps))
(+.f64 (.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 eps) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps eps) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (.f64 (.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))))
(+.f64 (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(+.f64 (.f64 (tan.f64 eps) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (.f64 eps (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))))
(-.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))))
(-.f64 #s(literal 0 binary64) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (/.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps))))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 (/.f64 (.f64 eps eps) (+.f64 eps (sin.f64 eps))) (-.f64 eps (tan.f64 eps))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))) (-.f64 eps (tan.f64 eps))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 (tan.f64 eps) eps)) (/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 (tan.f64 eps) eps)))
(-.f64 (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))) (/.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 eps eps (.f64 (sin.f64 eps) (+.f64 eps (sin.f64 eps)))))))
(-.f64 (/.f64 (.f64 eps eps) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 eps eps)))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))))
(-.f64 (/.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))) (/.f64 (.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps))) (.f64 (.f64 eps eps) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal -2 binary64))))) (/.f64 (pow.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) #s(literal 3 binary64)) (fma.f64 (/.f64 (sin.f64 eps) (-.f64 eps (tan.f64 eps))) (.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) (+.f64 eps (sin.f64 eps))) (.f64 (.f64 eps eps) (pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal -2 binary64))))))
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(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (+.f64 (fma.f64 eps (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (pow.f64 (.f64 eps (tan.f64 eps)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (tan.f64 eps) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))) (fma.f64 eps eps (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(pow.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 (-.f64 eps (tan.f64 eps)) #s(literal 1 binary64))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))) #s(literal 1 binary64)))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)))))
(*.f64 #s(literal 1 binary64) (-.f64 eps (tan.f64 eps)))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) #s(literal 1 binary64)))
(*.f64 (+.f64 eps (tan.f64 eps)) (/.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
(.f64 (+.f64 eps (tan.f64 eps)) (.f64 (-.f64 eps (tan.f64 eps)) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps)))))
(*.f64 #s(literal -1 binary64) (-.f64 (tan.f64 eps) eps))
(.f64 (neg.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps)))))
(.f64 (+.f64 (neg.f64 (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 eps (tan.f64 eps)))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))) (fma.f64 eps (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) (fma.f64 (tan.f64 eps) (-.f64 (tan.f64 eps) eps) (.f64 eps eps)))
(.f64 (/.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (-.f64 eps (tan.f64 eps)))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (fma.f64 eps (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps eps)) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 3 binary64)))) (fma.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (-.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) (.f64 eps eps)) (.f64 eps (.f64 eps (*.f64 eps eps)))))
(.f64 (/.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (pow.f64 (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps))) #s(literal 2 binary64)))) (-.f64 (.f64 eps eps) (.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)))))

simplify369.0ms (2%)

Memory

30.0MiB live, 579.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 288×	`lower-fma.f64`
12 288×	`lower-fma.f32`
6 122×	`lower-*.f64`
6 122×	`lower-*.f32`
1 424×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 43

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
1
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
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)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) (-.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (/ (* (pow (sin eps) 2) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 3) (pow (cos eps) 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(fma.f64 (sin.f64 eps) (fma.f64 (sin.f64 eps) (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 (.f64 eps eps) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) eps)) (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (.f64 eps eps)) (/.f64 #s(literal -1 binary64) eps)) #s(literal 1 binary64)))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (- (sin eps) (/ (sin eps) (cos eps))) eps)))
(fma.f64 (/.f64 (sin.f64 eps) eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))) #s(literal 1 binary64))
(+ 1 (* -1 (/ (- (+ (sin eps) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (cos eps)))) (/ (sin eps) (cos eps))) eps)))
(-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps) #s(literal -1 binary64)) (sin.f64 eps)) eps))
(+ 1 (* -1 (/ (- (+ (sin eps) (* -1 (/ (- (* -1 (/ (* (pow (sin eps) 2) (- (sin eps) (/ (sin eps) (cos eps)))) (* eps (pow (cos eps) 2)))) (/ (* (sin eps) (- (sin eps) (/ (sin eps) (cos eps)))) (cos eps))) eps))) (/ (sin eps) (cos eps))) eps)))
(+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps)))) (+.f64 (/.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (.f64 eps (pow.f64 (cos.f64 eps) #s(literal 2 binary64)))) (/.f64 (sin.f64 eps) (cos.f64 eps)))) eps) (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps))
(* 1/6 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal 1/6 binary64))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(-.f64 eps (sin.f64 eps))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(-.f64 eps (sin.f64 eps))
eps
(* eps (+ 1 (* -1/6 (pow eps 2))))
(fma.f64 eps (.f64 (.f64 eps eps) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* 1/120 (pow eps 2)) 1/6))))
(fma.f64 (.f64 eps (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) eps)
(* eps (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 1/120 (* -1/5040 (pow eps 2)))) 1/6))))
(fma.f64 (.f64 eps (.f64 eps eps)) (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)) 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)
(* -1/3 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/3 binary64))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps #s(literal -2/15 binary64)) #s(literal -1/3 binary64))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -17/315 binary64)) #s(literal -2/15 binary64)) #s(literal -1/3 binary64)))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -62/2835 binary64) #s(literal -17/315 binary64)) #s(literal -2/15 binary64))) #s(literal -1/3 binary64))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(-.f64 eps (/.f64 (sin.f64 eps) (cos.f64 eps)))

eval72.0ms (0.4%)

Memory: -9.9MiB live, 98.2MiB allocated
Compiler: Compiled 12 434 to 1 225 computations (90.1% saved)

prune133.0ms (0.7%)

Memory

-26.8MiB live, 191.4MiB allocated

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	454	8	462
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	454	9	463

Accuracy

100.0%

Counts

463 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
▶	99.8%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
	99.7%	(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
▶	1.0%	(/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))
✓	1.6%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
▶	0.5%	(/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
	1.7%	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
	0.5%	(.f64 (/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 eps (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))))
▶	99.0%	#s(literal -1/2 binary64)

Compiler

Compiled 298 to 180 computations (39.6% saved)

simplify258.0ms (1.4%)

Memory

34.0MiB live, 385.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	128	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))
✓	cost-diff	128	(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))
✓	cost-diff	384	(/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	7616	(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	cost-diff	128	(-.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
✓	cost-diff	128	(+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
✓	cost-diff	0	(*.f64 eps #s(literal -27/2800 binary64))
✓	cost-diff	0	(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
✓	cost-diff	0	(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Rules

7 966×	`lower-fma.f32`
7 954×	`lower-fma.f64`
3 116×	`lower-*.f32`
3 102×	`lower-*.f64`
1 478×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	281
0	68	274
1	146	271
2	356	271
3	927	266
4	2000	266
5	4124	266
6	7103	266
0	8115	255

Stop Event

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

Calls

Call 1

Inputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(*.f64 eps #s(literal 27/112000 binary64))
#s(literal 27/112000 binary64)
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
(/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
(-.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))))
(*.f64 eps eps)
eps
(/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps)))
#s(literal 1 binary64)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps)))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
(*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))
#s(literal 2 binary64)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(*.f64 eps #s(literal 27/112000 binary64))
#s(literal 27/112000 binary64)
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
#s(literal -1/2 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
(/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64)))
(-.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(fma.f64 eps eps #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64))) (+.f64 eps (sin.f64 eps)))
(*.f64 eps eps)
eps
(/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps)))
#s(literal 1 binary64)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) #s(literal -1/2 binary64)) (+.f64 eps (sin.f64 eps)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64)) (+.f64 eps (sin.f64 eps)))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps)))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
(*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))
#s(literal 2 binary64)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)

localize758.0ms (4.1%)

Memory

-3.0MiB live, 1 025.2MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	58.2%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))
✓	accuracy	49.7%	(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps)))
✓	accuracy	37.9%	(/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))
✓	accuracy	7.0%	(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))))
✓	accuracy	99.8%	(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
✓	accuracy	73.4%	(+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	29.6%	(/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	accuracy	100.0%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	99.4%	(*.f64 eps #s(literal -27/2800 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
✓	accuracy	99.9%	(*.f64 eps #s(literal 27/112000 binary64))
✓	accuracy	99.4%	(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))

Samples

524.0ms	133×	3	valid
72.0ms	67×	2	valid
68.0ms	49×	1	valid
28.0ms	6×	4	valid
0.0ms	1×	0	valid

Compiler

Compiled 295 to 43 computations (85.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 634.0ms

ival-tan: 163.0ms (25.7% of total)

ival-sin: 107.0ms (16.9% of total)

ival-cos: 99.0ms (15.6% of total)

ival-add: 81.0ms (12.8% of total)

ival-mult: 79.0ms (12.5% of total)

adjust: 53.0ms (8.4% of total)

ival-div: 18.0ms (2.8% of total)

const: 17.0ms (2.7% of total)

ival-sub: 11.0ms (1.7% of total)

ival-neg: 4.0ms (0.6% of total)

exact: 1.0ms (0.2% of total)

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

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

series30.0ms (0.2%)

Memory

25.6MiB live, 64.6MiB allocated

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))>
#<alt (*.f64 eps eps)>
#<alt (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))>
#<alt (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))>
#<alt (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))>
#<alt (fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))>
#<alt (*.f64 eps #s(literal -27/2800 binary64))>
#<alt (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))>
#<alt (-.f64 (*.f64 eps eps) #s(literal 1/2 binary64))>
#<alt (/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))>
#<alt (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))))>
#<alt (/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))>
#<alt (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))>
#<alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))>
#<alt (*.f64 eps #s(literal 27/112000 binary64))>
#<alt (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))>
#<alt (-.f64 eps (tan.f64 eps))>
#<alt (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))>
#<alt (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps)))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))>
#<alt (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 4))>
#<alt (* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* -27/2800 eps)>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* eps (- (* 27/112000 (pow eps 2)) 27/2800))>
#<alt (* 27/112000 (pow eps 3))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 3))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt (* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* -27/2800 (pow eps 4))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt (* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))>
#<alt 9/40>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (+ 9/40 (* -27/2800 (pow eps 2)))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* -27/2800 eps)>
#<alt (* 1/3 (pow eps 4))>
#<alt (* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt -1/2>
#<alt (- (pow eps 2) 1/2)>
#<alt (- (pow eps 2) 1/2)>
#<alt (- (pow eps 2) 1/2)>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt (- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) eps))))>
#<alt (* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps))))) (pow eps 2)))) (/ (sin eps) eps)))>
#<alt (* eps (- (+ 1 (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (* 2 eps))))) (pow (sin eps) 3)) (pow eps 3)))) (+ (* -1 (/ (pow (sin eps) 2) (pow eps 2))) (+ (* 1/2 (/ (- 1 (cos (* 2 eps))) (pow eps 2))) (/ (sin eps) eps)))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) eps) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (+ (* -1/2 (/ (- 1 (cos (neg (* -2 eps)))) eps)) (/ (pow (sin eps) 2) eps)) (sin eps)) eps)) 1)))>
#<alt (* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (neg (* -2 eps))))) eps)) (/ (pow (sin eps) 3) eps)) (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2))) eps)) (sin eps)) eps)) 1)))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps))))) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))>
#<alt (- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps))))) (pow eps 2))) (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (* 2 eps))))) (pow (sin eps) 3)) (pow eps 3)))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps)))))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps))))) (* (pow eps 3) (cos eps)))))))>
#<alt 1>
#<alt (- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))>
#<alt (+ 1 (* -1 (/ (- (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2)) eps))) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* eps (cos eps)))) eps)))>
#<alt (+ 1 (* -1 (/ (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (- (+ (* -1 (- (* -1 (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2))) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps)))) (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps)))))) (pow (sin eps) 3)) eps))) (/ (* (sin eps) (- (* -1 (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2))) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps)))) (* eps (cos eps)))) eps))) eps)))>
#<alt (* -1/2 eps)>
#<alt (* eps (- (* 1/8 (pow eps 2)) 1/2))>
#<alt (* eps (- (* (pow eps 2) (+ 1/8 (* -7/720 (pow eps 2)))) 1/2))>
#<alt (* eps (- (* (pow eps 2) (+ 1/8 (* (pow eps 2) (- (* 5/24192 (pow eps 2)) 7/720)))) 1/2))>
#<alt (* -1/2 (/ (- 1 (cos (* 2 eps))) eps))>
#<alt (/ (- (* 1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps))))) eps)>
#<alt (/ (- (* -1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2))) (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps)))))) eps)>
#<alt (/ (- (* 1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (* 2 eps)))) (pow eps 3))) (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2)))))) eps)>
#<alt (* -1/2 (/ (- 1 (cos (neg (* -2 eps)))) eps))>
#<alt (* -1 (/ (- (* -1/2 (/ (* (sin eps) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* -1/8 (pow eps 2))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* 7/720 (pow eps 2)) 1/8))))>
#<alt (* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 7/720 (* -5/24192 (pow eps 2)))) 1/8))))>
#<alt (* 1/2 (/ (- 1 (cos (* 2 eps))) eps))>
#<alt (/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps))))) eps)>
#<alt (/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2))))) eps)>
#<alt (/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* -1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (* 2 eps)))) (pow eps 3))) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2)))))) eps)>
#<alt (* 1/2 (/ (- 1 (cos (neg (* -2 eps)))) eps))>
#<alt (* -1 (/ (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (* 1/2 (/ (* (sin eps) (- 1 (cos (neg (* -2 eps))))) eps))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps)))))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))) eps))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps)))))) (* 1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (neg (* -2 eps))))) eps))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt (* 27/112000 eps)>
#<alt -27/2800>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -2/3 (pow eps 4))>
#<alt (* (pow eps 4) (- (* -19/90 (pow eps 2)) 2/3))>
#<alt (* (pow eps 4) (- (* (pow eps 2) (- (* -223/2520 (pow eps 2)) 19/90)) 2/3))>
#<alt (* (pow eps 4) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -8117/226800 (pow eps 2)) 223/2520)) 19/90)) 2/3))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))>
#<alt (* 2 (pow eps 2))>
#<alt (* (pow eps 2) (+ 2 (* -2/3 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 2 (* (pow eps 2) (- (* 4/45 (pow eps 2)) 2/3))))>
#<alt (* (pow eps 2) (+ 2 (* (pow eps 2) (- (* (pow eps 2) (+ 4/45 (* -2/315 (pow eps 2)))) 2/3))))>
#<alt (- 1 (cos (* 2 eps)))>
#<alt (- 1 (cos (* 2 eps)))>
#<alt (- 1 (cos (* 2 eps)))>
#<alt (- 1 (cos (* 2 eps)))>
#<alt (- 1 (cos (neg (* -2 eps))))>
#<alt (- 1 (cos (neg (* -2 eps))))>
#<alt (- 1 (cos (neg (* -2 eps))))>
#<alt (- 1 (cos (neg (* -2 eps))))>

Calls

57 calls:

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

rewrite153.0ms (0.8%)

Memory

-4.5MiB live, 303.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 718×	`lower-fma.f32`
1 706×	`lower-fma.f64`
1 548×	`lower-*.f32`
1 534×	`lower-*.f64`
1 204×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	205
0	68	201
1	316	183
0	2698	180

Stop Event

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

Counts

19 → 406

Calls

Call 1

Inputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(*.f64 eps #s(literal -27/2800 binary64))
(+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
(-.f64 (*.f64 eps eps) #s(literal 1/2 binary64))
(/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))))
(/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (*.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64)))
(*.f64 eps #s(literal 27/112000 binary64))
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(-.f64 eps (tan.f64 eps))
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps)))

Outputs
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))))
(+.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/2 binary64))
(+.f64 (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) (fma.f64 eps (.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(+.f64 (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)))) (.f64 eps (*.f64 eps #s(literal 9/40 binary64))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))))
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/2 binary64))
(fma.f64 eps (.f64 eps (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)))) (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(fma.f64 eps (.f64 (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
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(fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) eps #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) eps) eps (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)))) eps (fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))) (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))) #s(literal -1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))) #s(literal -1/8 binary64)) (-.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) #s(literal -1/2 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))) #s(literal -1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) (.f64 (*.f64 eps eps) #s(literal -1/2 binary64))))))
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(exp.f64 (*.f64 (log.f64 eps) #s(literal 2 binary64)))
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(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps eps))))) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64))))
(fma.f64 #s(literal -1 binary64) (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 eps eps)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps eps))))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 eps eps)) #s(literal 3 binary64))) (fma.f64 (cos.f64 (+.f64 eps eps)) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps eps)))))) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 eps eps)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) (+.f64 eps eps))))))) (neg.f64 (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64))))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (cos.f64 (+.f64 eps eps))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (neg.f64 (cos.f64 (+.f64 eps eps))) (neg.f64 (cos.f64 (+.f64 eps eps)))) (.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps eps)))))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (cos.f64 (+.f64 eps eps))) (neg.f64 (cos.f64 (+.f64 eps eps))))) (-.f64 #s(literal 1 binary64) (neg.f64 (cos.f64 (+.f64 eps eps)))))
(*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 (+.f64 eps eps)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 (+.f64 eps eps)) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(.f64 (-.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) (+.f64 eps eps)))))) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1 binary64))))

simplify396.0ms (2.1%)

Memory

-34.7MiB live, 667.7MiB allocated

Algorithm

1×	egg-herbie

Rules

8 928×	`lower-fma.f64`
8 928×	`lower-fma.f32`
5 032×	`lower-*.f64`
5 032×	`lower-*.f32`
3 138×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	498	3252
1	1502	3152
2	4505	2957
0	8288	2808

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 224

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 4))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* -27/2800 eps)
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(* 27/112000 (pow eps 3))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 3))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* -27/2800 (pow eps 4))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
9/40
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(+ 9/40 (* -27/2800 (pow eps 2)))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 (pow eps 2))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* -27/2800 eps)
(* 1/3 (pow eps 4))
(* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
-1/2
(- (pow eps 2) 1/2)
(- (pow eps 2) 1/2)
(- (pow eps 2) 1/2)
(pow eps 2)
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
(- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))
(+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) eps))))
(* eps (- (+ 1 (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps))))) (pow eps 2)))) (/ (sin eps) eps)))
(* eps (- (+ 1 (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (* 2 eps))))) (pow (sin eps) 3)) (pow eps 3)))) (+ (* -1 (/ (pow (sin eps) 2) (pow eps 2))) (+ (* 1/2 (/ (- 1 (cos (* 2 eps))) (pow eps 2))) (/ (sin eps) eps)))))
eps
(* -1 (* eps (- (/ (sin eps) eps) 1)))
(* -1 (* eps (- (* -1 (/ (- (+ (* -1/2 (/ (- 1 (cos (neg (* -2 eps)))) eps)) (/ (pow (sin eps) 2) eps)) (sin eps)) eps)) 1)))
(* -1 (* eps (- (* -1 (/ (- (* -1 (/ (- (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (neg (* -2 eps))))) eps)) (/ (pow (sin eps) 3) eps)) (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2))) eps)) (sin eps)) eps)) 1)))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps))))) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps))))))
(- (+ 1 (+ (* -1 (/ (sin eps) eps)) (+ (* -1 (/ (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps))))) (pow eps 2))) (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (* 2 eps))))) (pow (sin eps) 3)) (pow eps 3)))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* (pow eps 2) (cos eps)))) (* -1 (/ (* (sin eps) (- (* -1 (+ (* -1 (pow (sin eps) 2)) (* 1/2 (- 1 (cos (* 2 eps)))))) (* -1 (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps))))) (* (pow eps 3) (cos eps)))))))
1
(- (+ 1 (* -1 (/ (sin eps) eps))) (* -1 (/ (sin eps) (* eps (cos eps)))))
(+ 1 (* -1 (/ (- (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2)) eps))) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* eps (cos eps)))) eps)))
(+ 1 (* -1 (/ (+ (* -1 (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (* -1 (/ (- (+ (* -1 (- (* -1 (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2))) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps)))) (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps)))))) (pow (sin eps) 3)) eps))) (/ (* (sin eps) (- (* -1 (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (pow (sin eps) 2))) (/ (* (sin eps) (- (* -1 (sin eps)) (* -1 (/ (sin eps) (cos eps))))) (cos eps)))) (* eps (cos eps)))) eps))) eps)))
(* -1/2 eps)
(* eps (- (* 1/8 (pow eps 2)) 1/2))
(* eps (- (* (pow eps 2) (+ 1/8 (* -7/720 (pow eps 2)))) 1/2))
(* eps (- (* (pow eps 2) (+ 1/8 (* (pow eps 2) (- (* 5/24192 (pow eps 2)) 7/720)))) 1/2))
(* -1/2 (/ (- 1 (cos (* 2 eps))) eps))
(/ (- (* 1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps))))) eps)
(/ (- (* -1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2))) (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps)))))) eps)
(/ (- (* 1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (* 2 eps)))) (pow eps 3))) (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2)))))) eps)
(* -1/2 (/ (- 1 (cos (neg (* -2 eps)))) eps))
(* -1 (/ (- (* -1/2 (/ (* (sin eps) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(* 1/2 eps)
(* eps (+ 1/2 (* -1/8 (pow eps 2))))
(* eps (+ 1/2 (* (pow eps 2) (- (* 7/720 (pow eps 2)) 1/8))))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 7/720 (* -5/24192 (pow eps 2)))) 1/8))))
(* 1/2 (/ (- 1 (cos (* 2 eps))) eps))
(/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps))))) eps)
(/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2))))) eps)
(/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* -1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (* 2 eps)))) (pow eps 3))) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2)))))) eps)
(* 1/2 (/ (- 1 (cos (neg (* -2 eps)))) eps))
(* -1 (/ (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (* 1/2 (/ (* (sin eps) (- 1 (cos (neg (* -2 eps))))) eps))) eps))
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps)))))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))) eps))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps)))))) (* 1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (neg (* -2 eps))))) eps))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
(* 27/112000 eps)
-27/2800
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -2/3 (pow eps 4))
(* (pow eps 4) (- (* -19/90 (pow eps 2)) 2/3))
(* (pow eps 4) (- (* (pow eps 2) (- (* -223/2520 (pow eps 2)) 19/90)) 2/3))
(* (pow eps 4) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -8117/226800 (pow eps 2)) 223/2520)) 19/90)) 2/3))
(pow eps 2)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))
(* 2 (pow eps 2))
(* (pow eps 2) (+ 2 (* -2/3 (pow eps 2))))
(* (pow eps 2) (+ 2 (* (pow eps 2) (- (* 4/45 (pow eps 2)) 2/3))))
(* (pow eps 2) (+ 2 (* (pow eps 2) (- (* (pow eps 2) (+ 4/45 (* -2/315 (pow eps 2)))) 2/3))))
(- 1 (cos (* 2 eps)))
(- 1 (cos (* 2 eps)))
(- 1 (cos (* 2 eps)))
(- 1 (cos (* 2 eps)))
(- 1 (cos (neg (* -2 eps))))
(- 1 (cos (neg (* -2 eps))))
(- 1 (cos (neg (* -2 eps))))
(- 1 (cos (neg (* -2 eps))))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))))))
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
(pow eps 2)
(*.f64 eps eps)
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* 27/112000 (pow eps 4))
(.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* 27/112000 (pow eps 4))
(.f64 #s(literal 27/112000 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (.f64 (.f64 eps eps) (*.f64 eps eps)))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* (pow eps 4) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* eps (- (* 27/112000 (pow eps 2)) 27/2800))
(.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))
(* 27/112000 (pow eps 3))
(.f64 #s(literal 27/112000 binary64) (.f64 eps (*.f64 eps eps)))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* (pow eps 3) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* 27/112000 (pow eps 3))
(.f64 #s(literal 27/112000 binary64) (.f64 eps (*.f64 eps eps)))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
(* -1 (* (pow eps 3) (- (* 27/2800 (/ 1 (pow eps 2))) 27/112000)))
(.f64 (.f64 eps eps) (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps)))))
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 eps (.f64 eps #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))))
(* -27/2800 (pow eps 4))
(.f64 (.f64 eps eps) (.f64 eps (.f64 eps #s(literal -27/2800 binary64))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))))
(* (pow eps 4) (- (* 9/40 (/ 1 (pow eps 2))) (+ 27/2800 (/ 1/2 (pow eps 4)))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (+.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))))
9/40
#s(literal 9/40 binary64)
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(+ 9/40 (* -27/2800 (pow eps 2)))
(fma.f64 eps (*.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(* -27/2800 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(* -27/2800 (pow eps 2))
(.f64 eps (.f64 eps #s(literal -27/2800 binary64)))
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(* (pow eps 2) (- (* 9/40 (/ 1 (pow eps 2))) 27/2800))
(.f64 (.f64 (+.f64 #s(literal -27/2800 binary64) (/.f64 #s(literal 9/40 binary64) (*.f64 eps eps))) eps) eps)
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* -27/2800 eps)
(*.f64 eps #s(literal -27/2800 binary64))
(* 1/3 (pow eps 4))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal 1/3 binary64))
(* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (*.f64 eps eps) #s(literal -2/45 binary64) #s(literal 1/3 binary64)))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 1/315 binary64)) #s(literal -2/45 binary64)) #s(literal 1/3 binary64)))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -2/14175 binary64) #s(literal 1/315 binary64)) #s(literal -2/45 binary64)) #s(literal 1/3 binary64)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
-1/2
#s(literal -1/2 binary64)
(- (pow eps 2) 1/2)
(fma.f64 eps eps #s(literal -1/2 binary64))
(- (pow eps 2) 1/2)
(fma.f64 eps eps #s(literal -1/2 binary64))
(- (pow eps 2) 1/2)
(fma.f64 eps eps #s(literal -1/2 binary64))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 1 (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps))))
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
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eps
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1
#s(literal 1 binary64)
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#s(literal 1 binary64)
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(* eps (- (* 1/8 (pow eps 2)) 1/2))
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(/ (- (* -1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2))) (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps)))))) eps)
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(/ (- (* 1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (* 2 eps)))) (pow eps 3))) (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2)))))) eps)
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(/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) (/.f64 (sin.f64 eps) eps) #s(literal -1 binary64)) (cos.f64 (*.f64 eps #s(literal -2 binary64))))) eps)
(* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) eps) (.f64 (sin.f64 eps) (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))))) eps)
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* -1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (neg (* -2 eps))))) eps)) (* -1/2 (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(/.f64 (+.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (/.f64 (fma.f64 (sin.f64 eps) (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sin.f64 eps) (.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) (*.f64 (sin.f64 eps) (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) eps)))))) eps)) eps)) eps)
(* 1/2 eps)
(*.f64 eps #s(literal 1/2 binary64))
(* eps (+ 1/2 (* -1/8 (pow eps 2))))
(.f64 eps (fma.f64 (.f64 eps eps) #s(literal -1/8 binary64) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* 7/720 (pow eps 2)) 1/8))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 7/720 binary64) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* eps (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 7/720 (* -5/24192 (pow eps 2)))) 1/8))))
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -5/24192 binary64) #s(literal 7/720 binary64))) #s(literal -1/8 binary64)) #s(literal 1/2 binary64)))
(* 1/2 (/ (- 1 (cos (* 2 eps))) eps))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))) #s(literal 1/2 binary64)) eps)
(/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (* 1/2 (- 1 (cos (* 2 eps))))) eps)
(/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) (/.f64 (sin.f64 eps) eps) #s(literal -1 binary64)) (cos.f64 (*.f64 eps #s(literal -2 binary64))))) eps)
(/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2))))) eps)
(neg.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) eps) (.f64 (sin.f64 eps) (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))))) eps))
(/ (+ (* -1/2 (/ (* (sin eps) (- 1 (cos (* 2 eps)))) eps)) (+ (* -1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (* 2 eps)))) (pow eps 3))) (+ (* 1/2 (- 1 (cos (* 2 eps)))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (* 2 eps)))) (pow eps 2)))))) eps)
(/.f64 (+.f64 (neg.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) eps) (.f64 (sin.f64 eps) (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))))) (/.f64 (.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (.f64 eps (.f64 eps eps)))) eps)
(* 1/2 (/ (- 1 (cos (neg (* -2 eps)))) eps))
(/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))) #s(literal 1/2 binary64)) eps)
(* -1 (/ (+ (* -1/2 (- 1 (cos (neg (* -2 eps))))) (* 1/2 (/ (* (sin eps) (- 1 (cos (neg (* -2 eps))))) eps))) eps))
(/.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (fma.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) (/.f64 (sin.f64 eps) eps) #s(literal -1 binary64)) (cos.f64 (*.f64 eps #s(literal -2 binary64))))) eps)
(* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps)))))) (* 1/2 (/ (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps))))) eps))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(neg.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (fma.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))) eps) (.f64 (sin.f64 eps) (+.f64 #s(literal -1 binary64) (/.f64 (sin.f64 eps) eps))) (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64)))))) eps))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (pow (sin eps) 2) (- 1 (cos (neg (* -2 eps)))))) (* 1/2 (/ (* (pow (sin eps) 3) (- 1 (cos (neg (* -2 eps))))) eps))) eps)) (* -1/2 (* (sin eps) (- 1 (cos (neg (* -2 eps))))))) eps)) (* -1/2 (- 1 (cos (neg (* -2 eps)))))) eps))
(/.f64 (-.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (/.f64 (-.f64 (.f64 (sin.f64 eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (/.f64 (fma.f64 (pow.f64 (sin.f64 eps) #s(literal 2 binary64)) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 (pow.f64 (sin.f64 eps) #s(literal 3 binary64)) (/.f64 (fma.f64 #s(literal -1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal 1/2 binary64)) eps))) eps)) eps)) (neg.f64 eps))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
(* 27/112000 eps)
(*.f64 eps #s(literal 27/112000 binary64))
-27/2800
#s(literal -27/2800 binary64)
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 eps (.f64 eps (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps)))))
(* -1/3 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/3 binary64))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -2/15 binary64) #s(literal -1/3 binary64))))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -17/315 binary64) #s(literal -2/15 binary64)) #s(literal -1/3 binary64)))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -62/2835 binary64) #s(literal -17/315 binary64)) #s(literal -2/15 binary64)) #s(literal -1/3 binary64)))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(fma.f64 eps (neg.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps)))) eps)
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(fma.f64 eps (neg.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps)))) eps)
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(fma.f64 eps (neg.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps)))) eps)
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(fma.f64 eps (neg.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps)))) eps)
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(fma.f64 eps (neg.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps)))) eps)
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(fma.f64 eps (neg.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps)))) eps)
(* -2/3 (pow eps 4))
(.f64 eps (.f64 eps (.f64 (.f64 eps eps) #s(literal -2/3 binary64))))
(* (pow eps 4) (- (* -19/90 (pow eps 2)) 2/3))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal -19/90 binary64)) #s(literal -2/3 binary64)))
(* (pow eps 4) (- (* (pow eps 2) (- (* -223/2520 (pow eps 2)) 19/90)) 2/3))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -223/2520 binary64) #s(literal -19/90 binary64)) #s(literal -2/3 binary64)))
(* (pow eps 4) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -8117/226800 (pow eps 2)) 223/2520)) 19/90)) 2/3))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -8117/226800 binary64) #s(literal -223/2520 binary64)) #s(literal -19/90 binary64)) #s(literal -2/3 binary64)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(.f64 eps (fma.f64 eps (/.f64 (neg.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps) eps))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(.f64 eps (fma.f64 eps (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (sin.f64 eps) (.f64 eps eps))) (/.f64 (sin.f64 eps) eps)) eps))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(.f64 eps (fma.f64 eps (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (sin.f64 eps) (.f64 eps eps))) (/.f64 (sin.f64 eps) eps)) eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(.f64 eps (fma.f64 eps (/.f64 (neg.f64 (.f64 (sin.f64 eps) (-.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (cos.f64 eps))))) eps) eps))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))
(.f64 eps (fma.f64 eps (/.f64 (+.f64 (sin.f64 eps) (neg.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))))) eps) eps))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))
(.f64 eps (fma.f64 eps (/.f64 (+.f64 (sin.f64 eps) (neg.f64 (.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps))))) eps) eps))
(* 2 (pow eps 2))
(.f64 eps (.f64 eps #s(literal 2 binary64)))
(* (pow eps 2) (+ 2 (* -2/3 (pow eps 2))))
(.f64 (.f64 (fma.f64 (*.f64 eps eps) #s(literal -2/3 binary64) #s(literal 2 binary64)) eps) eps)
(* (pow eps 2) (+ 2 (* (pow eps 2) (- (* 4/45 (pow eps 2)) 2/3))))
(.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64))))
(* (pow eps 2) (+ 2 (* (pow eps 2) (- (* (pow eps 2) (+ 4/45 (* -2/315 (pow eps 2)))) 2/3))))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -2/315 binary64) #s(literal 4/45 binary64)) #s(literal -2/3 binary64)) #s(literal 2 binary64)))
(- 1 (cos (* 2 eps)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))
(- 1 (cos (* 2 eps)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))
(- 1 (cos (* 2 eps)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))
(- 1 (cos (* 2 eps)))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 eps))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 eps))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 eps))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))
(- 1 (cos (neg (* -2 eps))))
(-.f64 #s(literal 1 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))))

eval269.0ms (1.4%)

Memory: 6.3MiB live, 197.2MiB allocated
Compiler: Compiled 21 354 to 1 904 computations (91.1% saved)

prune76.0ms (0.4%)

Memory

15.5MiB live, 137.5MiB allocated

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	708	5	713
Fresh	2	1	3
Picked	2	3	5
Done	0	1	1
Total	712	10	722

Accuracy

100.0%

Counts

722 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.8%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
▶	99.7%	(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
▶	99.8%	(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
▶	0.5%	(/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
▶	1.0%	(/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	1.6%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
▶	1.7%	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
	1.0%	(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	99.0%	#s(literal -1/2 binary64)

Compiler

Compiled 353 to 181 computations (48.7% saved)

simplify406.0ms (2.2%)

Memory

-30.8MiB live, 467.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))
✓	cost-diff	0	(fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))
✓	cost-diff	0	(/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	cost-diff	128	(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
✓	cost-diff	0	(+.f64 eps eps)
✓	cost-diff	0	(cos.f64 (+.f64 eps eps))
✓	cost-diff	0	(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64)))
✓	cost-diff	0	(/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 eps (.f64 eps eps))
✓	cost-diff	0	(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
✓	cost-diff	0	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))
✓	cost-diff	0	(fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64))
✓	cost-diff	0	(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))

Rules

10 306×	`lower-fma.f32`
10 284×	`lower-fma.f64`
4 760×	`lower-*.f32`
4 748×	`lower-*.f64`
3 624×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	393
0	75	385
1	173	383
2	496	379
3	1592	379
4	2822	379
5	4182	379
6	5319	379
7	7810	379
0	8546	376

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))
(*.f64 eps eps)
eps
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))
#s(literal 27/112000 binary64)
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/4 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(.f64 eps (.f64 eps eps))
eps
(*.f64 eps eps)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64))
#s(literal -1/362880 binary64)
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64)))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
eps
#s(literal 1/2 binary64)
(fma.f64 eps eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))
eps
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
#s(literal -1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))
#s(literal 1/2 binary64)
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)

Outputs
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/20 binary64)) #s(literal 81/1600 binary64)) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/20 binary64)) #s(literal 81/1600 binary64)) #s(literal -1/4 binary64))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))
(*.f64 eps eps)
eps
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))
#s(literal 27/112000 binary64)
#s(literal -27/2800 binary64)
#s(literal 9/40 binary64)
#s(literal -1/4 binary64)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(*.f64 eps eps)
eps
#s(literal 9/40 binary64)
#s(literal -1/2 binary64)
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
(.f64 (.f64 eps (.f64 eps eps)) (/.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) (-.f64 eps (tan.f64 eps))))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(.f64 eps (.f64 eps eps))
eps
(*.f64 eps eps)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64))
(fma.f64 (*.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))
#s(literal -1/362880 binary64)
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64)))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
eps
#s(literal 1/2 binary64)
(fma.f64 eps eps #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64)))
eps
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))
#s(literal 1/2 binary64)
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)

localize668.0ms (3.6%)

Memory

39.0MiB live, 1 210.9MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	51.6%	(fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))
✓	accuracy	49.8%	(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
✓	accuracy	29.6%	(/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	accuracy	99.8%	(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
✓	accuracy	73.4%	(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64)))
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	29.6%	(/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	accuracy	99.8%	(.f64 eps (.f64 eps eps))
✓	accuracy	99.8%	(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	37.9%	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
✓	accuracy	100.0%	(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(*.f64 eps eps)
✓	accuracy	100.0%	(fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))
✓	accuracy	100.0%	(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))

Samples

406.0ms	133×	3	valid
111.0ms	67×	2	valid
39.0ms	49×	1	valid
16.0ms	6×	4	valid
0.0ms	1×	0	valid

Compiler

Compiled 436 to 49 computations (88.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 500.0ms

ival-tan: 144.0ms (28.8% of total)

adjust: 111.0ms (22.2% of total)

ival-cos: 109.0ms (21.8% of total)

ival-mult: 40.0ms (8% of total)

const: 39.0ms (7.8% of total)

ival-add: 37.0ms (7.4% of total)

ival-div: 13.0ms (2.6% of total)

ival-sub: 4.0ms (0.8% of total)

ival-sin: 2.0ms (0.4% of total)

exact: 1.0ms (0.2% of total)

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

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

series21.0ms (0.1%)

Memory

16.9MiB live, 56.2MiB allocated

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64))>
#<alt (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))>
#<alt (*.f64 eps eps)>
#<alt (fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))>
#<alt (/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))>
#<alt (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))>
#<alt (.f64 eps (.f64 eps eps))>
#<alt (/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))>
#<alt (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64)))>
#<alt (cos.f64 (+.f64 eps eps))>
#<alt (+.f64 eps eps)>
#<alt (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))>
#<alt (/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))>
#<alt (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))>
#<alt (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))>
#<alt (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))>
#<alt (-.f64 eps (tan.f64 eps))>
#<alt (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))>

Outputs
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))>
#<alt -1/4>
#<alt (- (* 81/1600 (pow eps 4)) 1/4)>
#<alt (- (* (pow eps 4) (+ 81/1600 (* -243/56000 (pow eps 2)))) 1/4)>
#<alt (- (* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* 3159/15680000 (pow eps 2)) 243/56000)))) 1/4)>
#<alt (* 729/12544000000 (pow eps 12))>
#<alt (* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))>
#<alt (* 729/12544000000 (pow eps 12))>
#<alt (* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 6))>
#<alt (* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 9/40 (pow eps 2))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt (* -1/362880 (pow eps 9))>
#<alt (* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 9) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 9))>
#<alt (* -1 (* (pow eps 9) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt (pow eps 3)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt (- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))>
#<alt (* 1/3 (pow eps 4))>
#<alt (* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt 1>
#<alt (+ 1 (* -2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 2/3 (pow eps 2)) 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* -4/45 (pow eps 2)))) 2)))>
#<alt (cos (* 2 eps))>
#<alt (cos (* 2 eps))>
#<alt (cos (* 2 eps))>
#<alt (cos (* 2 eps))>
#<alt (cos (neg (* -2 eps)))>
#<alt (cos (neg (* -2 eps)))>
#<alt (cos (neg (* -2 eps)))>
#<alt (cos (neg (* -2 eps)))>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* 2 eps)>
#<alt (* -1 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3 (pow eps 2)) 1))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2)))) 1))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45)))) 1))>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt (- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))>
#<alt (* 1/3 (pow eps 4))>
#<alt (* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 (pow eps 2)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* 1/3 (pow eps 2)) 1)))>
#<alt (+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2)))) 1)))>
#<alt (* 1/2 (cos (* 2 eps)))>
#<alt (* 1/2 (cos (* 2 eps)))>
#<alt (* 1/2 (cos (* 2 eps)))>
#<alt (* 1/2 (cos (* 2 eps)))>
#<alt (* 1/2 (cos (neg (* -2 eps))))>
#<alt (* 1/2 (cos (neg (* -2 eps))))>
#<alt (* 1/2 (cos (neg (* -2 eps))))>
#<alt (* 1/2 (cos (neg (* -2 eps))))>
#<alt -27/2800>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (- (* 27/112000 (pow eps 2)) 27/2800)>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* 27/112000 (pow eps 2))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -2/3 (pow eps 4))>
#<alt (* (pow eps 4) (- (* -19/90 (pow eps 2)) 2/3))>
#<alt (* (pow eps 4) (- (* (pow eps 2) (- (* -223/2520 (pow eps 2)) 19/90)) 2/3))>
#<alt (* (pow eps 4) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -8117/226800 (pow eps 2)) 223/2520)) 19/90)) 2/3))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))>
#<alt (* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))>

Calls

57 calls:

Time	Variable		Point	Expression
3.0ms	eps	@	0	(/ (* (* eps (* eps eps)) (+ (* (* eps eps) (+ (* (* eps eps) (+ (* (* eps eps) -1/362880) 1/5040)) -1/120)) 1/6)) (- eps (tan eps)))
1.0ms	eps	@	inf	(/ (* (* eps (* eps eps)) (+ (* (* eps eps) (+ (* (* eps eps) (+ (* (* eps eps) -1/362880) 1/5040)) -1/120)) 1/6)) (- eps (tan eps)))
1.0ms	eps	@	-inf	(/ (* (* eps (* eps eps)) (+ (* (* eps eps) (+ (* (* eps eps) (+ (* (* eps eps) -1/362880) 1/5040)) -1/120)) 1/6)) (- eps (tan eps)))
1.0ms	eps	@	inf	(/ (+ (* (* (* eps eps) (+ (* (* eps eps) (+ (* (* eps eps) 27/112000) -27/2800)) 9/40)) (* (* eps eps) (+ (* (* eps eps) (+ (* (* eps eps) 27/112000) -27/2800)) 9/40))) -1/4) (+ (* (* eps eps) (+ (* (* eps eps) (+ (* (* eps eps) 27/112000) -27/2800)) 9/40)) 1/2))
1.0ms	eps	@	-inf	(* eps (* eps eps))

rewrite379.0ms (2%)

Memory

-17.1MiB live, 671.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 110×	`lower-/.f32`
5 104×	`lower-/.f64`
4 456×	`lower-*.f32`
4 444×	`lower-*.f64`
3 224×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	261
0	75	227
1	388	208
2	3186	208
0	8883	205

Stop Event

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

Counts

19 → 773

Calls

Call 1

Inputs
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64))
(.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)))
(*.f64 eps eps)
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(.f64 eps (.f64 eps eps))
(/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64)))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
(+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))
(/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))))
(*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))
(fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64))
(-.f64 eps (tan.f64 eps))
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) #s(literal -1/2 binary64))
(+.f64 (.f64 (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) (.f64 eps (.f64 eps (.f64 eps eps)))) (-.f64 (.f64 eps (*.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(-.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))))) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) #s(literal 4 binary64)) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)))) #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))) (/.f64 (/.f64 #s(literal 1/16 binary64) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)))) #s(literal 1/4 binary64))) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))) (/.f64 (fma.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)))) #s(literal -1/4 binary64)) (neg.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) #s(literal 4 binary64)) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)))) #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/16 binary64) (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 eps eps) (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)))) #s(literal 1/4 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)))))) (fma.f64 eps (.f64 eps (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))))) (/.f64 #s(literal 1/8 binary64) (fma.f64 eps (.f64 eps (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))))) (+.f64 #s(literal 1/4 binary64) (.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) #s(literal 1/2 binary64)))))))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) #s(literal -1/2 binary64))
(fma.f64 eps (.f64 eps (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))))) (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 eps (.f64 (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) (.f64 eps eps)) (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 eps (pow.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))) (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps eps) (pow.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(fma.f64 (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) (.f64 eps (.f64 eps (.f64 eps eps))) (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))) (.f64 eps eps) (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)) (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) eps #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64)))) eps) eps (-.f64 (.f64 eps (.f64 eps #s(literal 9/40 binary64))) #s(literal 1/2 binary64)))
(fma.f64 (pow.f64 (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64))) #s(literal 1 binary64)) eps #s(literal -1/2 binary64))
(fma.f64 (pow.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1 binary64)) (*.f64 eps eps) #s(literal -1/2 binary64))
(neg.f64 (/.f64 (fma.f64 (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) (.f64 (.f64 eps eps) (.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)))) #s(literal -1/4 binary64)) (neg.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))))
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(/.f64 (fma.f64 (.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (+.f64 eps (tan.f64 eps)) (.f64 (+.f64 eps (tan.f64 eps)) (.f64 eps (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))))) (.f64 (+.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
(/.f64 (fma.f64 (.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (.f64 (+.f64 eps (tan.f64 eps)) (.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) eps))) (.f64 (+.f64 eps (tan.f64 eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps))))
(/.f64 (fma.f64 (.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (sin.f64 eps)) (+.f64 eps (tan.f64 eps)) (.f64 (+.f64 eps (tan.f64 eps)) (.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) eps))) (.f64 (+.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
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(/.f64 (neg.f64 (.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (fma.f64 eps (.f64 eps eps) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))))) (neg.f64 (.f64 (+.f64 eps (tan.f64 eps)) (fma.f64 (sin.f64 eps) (-.f64 (sin.f64 eps) eps) (*.f64 eps eps)))))
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(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (neg.f64 (.f64 (fma.f64 (sin.f64 eps) (-.f64 (sin.f64 eps) eps) (.f64 eps eps)) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps)))))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) #s(literal 2 binary64)) (pow.f64 (.f64 (-.f64 eps (tan.f64 eps)) (sin.f64 eps)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 eps (-.f64 eps (tan.f64 eps))) (.f64 (-.f64 eps (tan.f64 eps)) (sin.f64 eps)))))
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(/.f64 (neg.f64 (.f64 (-.f64 eps (tan.f64 eps)) (-.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))))) (neg.f64 (-.f64 eps (sin.f64 eps))))
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(/.f64 (neg.f64 (.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (+.f64 eps (sin.f64 eps)))) (neg.f64 (+.f64 eps (tan.f64 eps))))
(/.f64 (neg.f64 (.f64 (fma.f64 eps (.f64 eps eps) (pow.f64 (sin.f64 eps) #s(literal 3 binary64))) (-.f64 eps (tan.f64 eps)))) (neg.f64 (fma.f64 (sin.f64 eps) (-.f64 (sin.f64 eps) eps) (*.f64 eps eps))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 eps eps) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (-.f64 eps (tan.f64 eps)))) (neg.f64 (-.f64 eps (sin.f64 eps))))
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(*.f64 (+.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

simplify602.0ms (3.2%)

Memory

-6.7MiB live, 381.4MiB allocated

Algorithm

1×	egg-herbie

Rules

11 070×	`lower-fma.f64`
11 070×	`lower-fma.f32`
5 504×	`lower-+.f64`
5 504×	`lower-+.f32`
4 528×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	367	3043
1	1011	2962
2	2977	2838
0	8122	2696

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 226

Calls

Call 1

Inputs
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
-1/4
(- (* 81/1600 (pow eps 4)) 1/4)
(- (* (pow eps 4) (+ 81/1600 (* -243/56000 (pow eps 2)))) 1/4)
(- (* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* 3159/15680000 (pow eps 2)) 243/56000)))) 1/4)
(* 729/12544000000 (pow eps 12))
(* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))
(* 729/12544000000 (pow eps 12))
(* (pow eps 12) (- 729/12544000000 (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (* 729/156800000 (/ 1 (pow eps 2)))))
(* (pow eps 12) (- (+ 729/12544000000 (/ 3159/15680000 (pow eps 4))) (+ (* 729/156800000 (/ 1 (pow eps 2))) (* 243/56000 (/ 1 (pow eps 6))))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 6))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(- (* 9/40 (pow eps 2)) 1/2)
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* 9/40 (pow eps 2))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 9/40 (* 1/2 (/ 1 (pow eps 2)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(* -1/362880 (pow eps 9))
(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 9) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 9))
(* -1 (* (pow eps 9) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
(pow eps 3)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
(- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))
(+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))
(* 1/3 (pow eps 4))
(* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
1
(+ 1 (* -2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 2/3 (pow eps 2)) 2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* -4/45 (pow eps 2)))) 2)))
(cos (* 2 eps))
(cos (* 2 eps))
(cos (* 2 eps))
(cos (* 2 eps))
(cos (neg (* -2 eps)))
(cos (neg (* -2 eps)))
(cos (neg (* -2 eps)))
(cos (neg (* -2 eps)))
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* 2 eps)
(* -1 (pow eps 2))
(* (pow eps 2) (- (* 1/3 (pow eps 2)) 1))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2)))) 1))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45)))) 1))
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
(- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))
(+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))
(* 1/3 (pow eps 4))
(* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
1/2
(+ 1/2 (* -1 (pow eps 2)))
(+ 1/2 (* (pow eps 2) (- (* 1/3 (pow eps 2)) 1)))
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2)))) 1)))
(* 1/2 (cos (* 2 eps)))
(* 1/2 (cos (* 2 eps)))
(* 1/2 (cos (* 2 eps)))
(* 1/2 (cos (* 2 eps)))
(* 1/2 (cos (neg (* -2 eps))))
(* 1/2 (cos (neg (* -2 eps))))
(* 1/2 (cos (neg (* -2 eps))))
(* 1/2 (cos (neg (* -2 eps))))
-27/2800
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(- (* 27/112000 (pow eps 2)) 27/2800)
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* 27/112000 (pow eps 2))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -2/3 (pow eps 4))
(* (pow eps 4) (- (* -19/90 (pow eps 2)) 2/3))
(* (pow eps 4) (- (* (pow eps 2) (- (* -223/2520 (pow eps 2)) 19/90)) 2/3))
(* (pow eps 4) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -8117/226800 (pow eps 2)) 223/2520)) 19/90)) 2/3))
(pow eps 2)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))) (-.f64 (/.f64 #s(literal 27/2800 binary64) (*.f64 eps eps)) #s(literal 27/112000 binary64))))
(* 27/112000 (pow eps 6))
(*.f64 #s(literal 27/112000 binary64) (pow.f64 eps #s(literal 6 binary64)))
(* (pow eps 6) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (+.f64 (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (.f64 eps eps))) (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (*.f64 eps eps)))))
(* (pow eps 6) (- (+ 27/112000 (/ 9/40 (pow eps 4))) (+ (* 27/2800 (/ 1 (pow eps 2))) (* 1/2 (/ 1 (pow eps 6))))))
(.f64 (pow.f64 eps #s(literal 6 binary64)) (-.f64 (+.f64 (/.f64 #s(literal 9/40 binary64) (.f64 (.f64 eps eps) (.f64 eps eps))) (/.f64 #s(literal -1/2 binary64) (pow.f64 eps #s(literal 6 binary64)))) (-.f64 (/.f64 #s(literal 27/2800 binary64) (*.f64 eps eps)) #s(literal 27/112000 binary64))))
-1/4
#s(literal -1/4 binary64)
(- (* 81/1600 (pow eps 4)) 1/4)
(fma.f64 (.f64 (.f64 eps eps) (*.f64 eps eps)) #s(literal 81/1600 binary64) #s(literal -1/4 binary64))
(- (* (pow eps 4) (+ 81/1600 (* -243/56000 (pow eps 2)))) 1/4)
(fma.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (.f64 eps eps) #s(literal -243/56000 binary64) #s(literal 81/1600 binary64)) #s(literal -1/4 binary64))
(- (* (pow eps 4) (+ 81/1600 (* (pow eps 2) (- (* 3159/15680000 (pow eps 2)) 243/56000)))) 1/4)
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(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 (pow eps 2)))
(-.f64 #s(literal 1/2 binary64) (*.f64 eps eps))
(+ 1/2 (* (pow eps 2) (- (* 1/3 (pow eps 2)) 1)))
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/3 binary64) #s(literal -1 binary64))) #s(literal 1/2 binary64))
(+ 1/2 (* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2)))) 1)))
(fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -2/45 binary64)) #s(literal 1/3 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64))
(* 1/2 (cos (* 2 eps)))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
(* 1/2 (cos (* 2 eps)))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
(* 1/2 (cos (* 2 eps)))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
(* 1/2 (cos (* 2 eps)))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
(* 1/2 (cos (neg (* -2 eps))))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
(* 1/2 (cos (neg (* -2 eps))))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
(* 1/2 (cos (neg (* -2 eps))))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
(* 1/2 (cos (neg (* -2 eps))))
(.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))))
-27/2800
#s(literal -27/2800 binary64)
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(- (* 27/112000 (pow eps 2)) 27/2800)
(fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* 27/112000 (pow eps 2))
(.f64 (.f64 eps eps) #s(literal 27/112000 binary64))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* (pow eps 2) (- 27/112000 (* 27/2800 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps eps) (+.f64 #s(literal 27/112000 binary64) (/.f64 #s(literal -27/2800 binary64) (*.f64 eps eps))))
(* -1/3 (pow eps 3))
(.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/3 binary64))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) #s(literal -2/15 binary64) #s(literal -1/3 binary64)))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal -17/315 binary64) #s(literal -2/15 binary64)) #s(literal -1/3 binary64))))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
(.f64 (.f64 eps eps) (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -62/2835 binary64) #s(literal -17/315 binary64)) #s(literal -2/15 binary64)) #s(literal -1/3 binary64))))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(fma.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps))) (neg.f64 eps) eps)
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(fma.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps))) (neg.f64 eps) eps)
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(fma.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps))) (neg.f64 eps) eps)
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(fma.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps))) (neg.f64 eps) eps)
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(fma.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps))) (neg.f64 eps) eps)
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(fma.f64 (/.f64 (sin.f64 eps) (*.f64 eps (cos.f64 eps))) (neg.f64 eps) eps)
(* -2/3 (pow eps 4))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) #s(literal -2/3 binary64))
(* (pow eps 4) (- (* -19/90 (pow eps 2)) 2/3))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 eps (*.f64 eps #s(literal -19/90 binary64)) #s(literal -2/3 binary64)))
(* (pow eps 4) (- (* (pow eps 2) (- (* -223/2520 (pow eps 2)) 19/90)) 2/3))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal -223/2520 binary64) #s(literal -19/90 binary64))) #s(literal -2/3 binary64)))
(* (pow eps 4) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -8117/226800 (pow eps 2)) 223/2520)) 19/90)) 2/3))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -8117/226800 binary64) #s(literal -223/2520 binary64))) #s(literal -19/90 binary64)) #s(literal -2/3 binary64)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(.f64 (.f64 eps eps) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps) #s(literal 1 binary64)))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(.f64 eps (fma.f64 eps (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (sin.f64 eps) (.f64 eps eps))) (/.f64 (sin.f64 eps) eps)) eps))
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (/ (sin eps) eps)))))
(.f64 eps (fma.f64 eps (fma.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (-.f64 (/.f64 #s(literal -1 binary64) eps) (/.f64 (sin.f64 eps) (.f64 eps eps))) (/.f64 (sin.f64 eps) eps)) eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (/ (sin eps) eps))))
(.f64 (.f64 eps eps) (fma.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps) #s(literal 1 binary64)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))
(.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (neg.f64 (sin.f64 eps)) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))) eps)))
(* (pow eps 2) (+ 1 (* -1 (/ (+ (* -1 (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (/ (pow (sin eps) 2) (* eps (cos eps)))) eps))))
(.f64 (.f64 eps eps) (-.f64 #s(literal 1 binary64) (/.f64 (+.f64 (neg.f64 (sin.f64 eps)) (*.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (+.f64 #s(literal 1 binary64) (/.f64 (sin.f64 eps) eps)))) eps)))

eval339.0ms (1.8%)

Memory: 5.8MiB live, 369.0MiB allocated
Compiler: Compiled 68 171 to 3 190 computations (95.3% saved)

prune271.0ms (1.5%)

Memory

3.4MiB live, 322.1MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	1 583	2	1 585
Fresh	0	1	1
Picked	3	2	5
Done	0	4	4
Total	1 586	9	1 595

Accuracy

100.0%

Counts

1 595 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.8%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.7%	(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
✓	99.8%	(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
▶	1.0%	(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	1.6%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
▶	1.7%	(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
▶	1.0%	(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	99.0%	#s(literal -1/2 binary64)

Compiler

Compiled 175 to 91 computations (48% saved)

simplify262.0ms (1.4%)

Memory

-0.8MiB live, 558.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(cos.f64 (+.f64 eps eps))
✓	cost-diff	0	(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
✓	cost-diff	0	(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	cost-diff	0	(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
✓	cost-diff	0	(.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps)
✓	cost-diff	0	(.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps))
✓	cost-diff	0	(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
✓	cost-diff	0	(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 eps eps)
✓	cost-diff	0	(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	cost-diff	1472	(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))

Rules

6 630×	`lower-fma.f32`
6 618×	`lower-fma.f64`
3 960×	`lower-*.f32`
3 946×	`lower-*.f64`
2 186×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	289
0	65	289
1	147	285
2	410	285
3	1267	275
4	3394	275
5	6208	275
0	8092	271

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 eps eps)
eps
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))
#s(literal 1/2 binary64)
(+.f64 (cos.f64 (*.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64))
(cos.f64 (*.f64 eps #s(literal -2 binary64)))
(*.f64 eps #s(literal -2 binary64))
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
(.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps))
(.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(*.f64 eps eps)
eps
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))
(*.f64 eps #s(literal -1/362880 binary64))
#s(literal -1/362880 binary64)
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
eps
(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)

Outputs
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) (fma.f64 eps eps #s(literal -1/2 binary64))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 eps #s(literal -2 binary64))) (fma.f64 eps eps #s(literal -1/2 binary64)))
(*.f64 eps eps)
eps
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) (.f64 eps eps)) #s(literal 1 binary64))
(/.f64 #s(literal 1/2 binary64) (*.f64 eps eps))
#s(literal 1/2 binary64)
(+.f64 (cos.f64 (*.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64))
(cos.f64 (*.f64 eps #s(literal -2 binary64)))
(*.f64 eps #s(literal -2 binary64))
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal 1 binary64)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)
(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
(/.f64 (.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))))) (-.f64 eps (tan.f64 eps)))
(.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps))
(.f64 eps (.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))))
(.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps)
(.f64 eps (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)))
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(*.f64 eps eps)
eps
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64))
(fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64))
(fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))
(*.f64 eps #s(literal -1/362880 binary64))
#s(literal -1/362880 binary64)
#s(literal 1/5040 binary64)
#s(literal -1/120 binary64)
#s(literal 1/6 binary64)
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) (fma.f64 eps eps #s(literal -1/2 binary64)))
eps
(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)) #s(literal -1/2 binary64))
(cos.f64 (+.f64 eps eps))
(+.f64 eps eps)
#s(literal 1/2 binary64)
#s(literal -1/2 binary64)
(*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps)))
(-.f64 eps (tan.f64 eps))
(tan.f64 eps)
(+.f64 eps (sin.f64 eps))
(sin.f64 eps)

localize621.0ms (3.3%)

Memory

4.5MiB live, 1 045.0MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	51.6%	(fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
✓	accuracy	49.8%	(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
✓	accuracy	29.6%	(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	accuracy	99.5%	(.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps)
✓	accuracy	99.3%	(*.f64 eps #s(literal -1/362880 binary64))
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	37.9%	(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
✓	accuracy	66.8%	(-.f64 eps (tan.f64 eps))
✓	accuracy	49.7%	(+.f64 (cos.f64 (*.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64))
✓	accuracy	29.6%	(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	accuracy	4.3%	(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))

Samples

387.0ms	136×	2	valid
97.0ms	30×	3	valid
64.0ms	89×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 314 to 42 computations (86.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 504.0ms

ival-cos: 177.0ms (35.1% of total)

ival-tan: 167.0ms (33.2% of total)

const: 37.0ms (7.3% of total)

adjust: 34.0ms (6.7% of total)

ival-mult: 33.0ms (6.6% of total)

ival-add: 25.0ms (5% of total)

ival-div: 24.0ms (4.8% of total)

ival-sub: 4.0ms (0.8% of total)

ival-sin: 2.0ms (0.4% of total)

exact: 1.0ms (0.2% of total)

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

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

series18.0ms (0.1%)

Memory

7.3MiB live, 49.8MiB allocated

Counts

15 → 180

Calls

Call 1

Inputs
#<alt (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))>
#<alt (/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))>
#<alt (*.f64 eps eps)>
#<alt (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))>
#<alt (/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))>
#<alt (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps))>
#<alt (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps)>
#<alt (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))>
#<alt (/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))>
#<alt (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))>
#<alt (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))>
#<alt (cos.f64 (+.f64 eps eps))>
#<alt (+.f64 (cos.f64 (*.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64))>
#<alt (-.f64 eps (tan.f64 eps))>
#<alt (*.f64 eps #s(literal -1/362880 binary64))>

Outputs
#<alt (* 1/3 (pow eps 4))>
#<alt (* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))>
#<alt (* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (- (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (/ (sin eps) eps)))))>
#<alt (- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (- (cos (* -2 eps)) 1)) (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (/ (sin eps) eps)))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1/2 (/ (- (cos (* -2 eps)) 1) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1/2 (- (cos (* -2 eps)) 1)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1/2 (- (cos (* -2 eps)) 1)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (pow eps 2)>
#<alt (* 1/3 (pow eps 2))>
#<alt (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2))))>
#<alt (* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))>
#<alt (* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))>
#<alt (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))>
#<alt (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))>
#<alt 1>
#<alt (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))>
#<alt (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))>
#<alt (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))>
#<alt (* -1/362880 (pow eps 8))>
#<alt (* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))>
#<alt (* 1/6 (pow eps 3))>
#<alt (* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt (* -1/362880 (pow eps 9))>
#<alt (* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 9) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 9))>
#<alt (* -1 (* (pow eps 9) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))>
#<alt (* 1/6 eps)>
#<alt (* eps (+ 1/6 (* -1/120 (pow eps 2))))>
#<alt (* eps (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))>
#<alt (* eps (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))>
#<alt (* -1/362880 (pow eps 7))>
#<alt (* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 7) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 7))>
#<alt (* -1 (* (pow eps 7) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))>
#<alt (* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))>
#<alt 1/6>
#<alt (+ 1/6 (* -1/120 (pow eps 2)))>
#<alt (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))>
#<alt (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120)))>
#<alt (* -1/362880 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* -1/362880 (pow eps 6))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))>
#<alt (* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt (* (pow eps 6) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))>
#<alt -1/2>
#<alt (- (* 9/40 (pow eps 2)) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)>
#<alt (- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt (- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))>
#<alt 1>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))>
#<alt (+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))>
#<alt (+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))>
#<alt (* 1/3 (pow eps 4))>
#<alt (* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))>
#<alt (* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (pow eps 2)>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* -1 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 1/3 (pow eps 2)) 1))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2)))) 1))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45)))) 1))>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (* 2 eps))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)>
#<alt 1>
#<alt (+ 1 (* -2 (pow eps 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* 2/3 (pow eps 2)) 2)))>
#<alt (+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* -4/45 (pow eps 2)))) 2)))>
#<alt (cos (* 2 eps))>
#<alt (cos (* 2 eps))>
#<alt (cos (* 2 eps))>
#<alt (cos (* 2 eps))>
#<alt (cos (neg (* -2 eps)))>
#<alt (cos (neg (* -2 eps)))>
#<alt (cos (neg (* -2 eps)))>
#<alt (cos (neg (* -2 eps)))>
#<alt (* -2 (pow eps 2))>
#<alt (* (pow eps 2) (- (* 2/3 (pow eps 2)) 2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* -4/45 (pow eps 2)))) 2))>
#<alt (* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* (pow eps 2) (- (* 2/315 (pow eps 2)) 4/45)))) 2))>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (- (cos (* -2 eps)) 1)>
#<alt (* -1/3 (pow eps 3))>
#<alt (* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))>
#<alt (* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))>
#<alt eps>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt (* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))>
#<alt eps>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>
#<alt (* -1/362880 eps)>

Calls

45 calls:

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

rewrite340.0ms (1.8%)

Memory

15.0MiB live, 527.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 422×	`lower-/.f32`
5 414×	`lower-/.f64`
4 674×	`lower-*.f32`
4 660×	`lower-*.f64`
3 096×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	197
0	65	197
1	298	193
2	2502	193
0	8618	190

Stop Event

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

Counts

15 → 551

Calls

Call 1

Inputs
(.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(*.f64 eps eps)
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
(.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps))
(.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (*.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))
(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64)))
(fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))
(cos.f64 (+.f64 eps eps))
(+.f64 (cos.f64 (*.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64))
(-.f64 eps (tan.f64 eps))
(*.f64 eps #s(literal -1/362880 binary64))

Outputs
(+.f64 (.f64 eps eps) (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (*.f64 eps eps)))
(+.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) (*.f64 eps eps))
(-.f64 (/.f64 (pow.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) (.f64 eps eps))) (/.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (-.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) (*.f64 eps eps))))
(fma.f64 eps eps (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))
(fma.f64 eps (.f64 eps #s(literal 1 binary64)) (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (*.f64 eps eps)))
(fma.f64 eps (.f64 eps (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps))) (.f64 eps eps))
(fma.f64 (.f64 eps eps) #s(literal 1 binary64) (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (*.f64 eps eps)))
(fma.f64 (.f64 eps eps) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 eps eps))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (.f64 (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) (.f64 eps eps)) (*.f64 eps eps))
(fma.f64 (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (.f64 eps eps)) (*.f64 eps eps))
(fma.f64 #s(literal 1 binary64) (.f64 eps eps) (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (*.f64 eps eps)))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 eps eps) (.f64 eps eps))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)) (/.f64 (.f64 eps eps) #s(literal 1 binary64)) (.f64 eps eps))
(fma.f64 (/.f64 (.f64 eps eps) #s(literal 1 binary64)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)) (.f64 eps eps))
(fma.f64 (.f64 #s(literal 1 binary64) eps) eps (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (*.f64 eps eps)))
(fma.f64 (.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)) eps) eps (.f64 eps eps))
(fma.f64 (.f64 (.f64 eps eps) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) (*.f64 eps eps))
(fma.f64 (.f64 (.f64 eps eps) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (*.f64 eps eps))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) eps) (/.f64 (.f64 eps eps) eps) (*.f64 eps eps))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) eps) (/.f64 (.f64 eps eps) (.f64 eps #s(literal 1 binary64))) (.f64 eps eps))
(fma.f64 (exp.f64 (log.f64 eps)) (exp.f64 (log.f64 eps)) (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 (.f64 eps eps) (.f64 eps eps)) (.f64 eps eps))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 #s(literal 1 binary64) eps)) (/.f64 (.f64 eps eps) eps) (.f64 eps eps))
(fma.f64 (/.f64 (.f64 eps eps) eps) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) eps) (*.f64 eps eps))
(fma.f64 (/.f64 (.f64 eps eps) eps) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps #s(literal 1 binary64))) (.f64 eps eps))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 eps eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (.f64 eps eps))
(fma.f64 (/.f64 (.f64 eps eps) (.f64 #s(literal 1 binary64) eps)) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) eps) (.f64 eps eps))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) #s(literal 3 binary64)) (.f64 (.f64 eps eps) (.f64 eps (.f64 eps (.f64 eps eps))))) (+.f64 (pow.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 (.f64 eps (.f64 eps (.f64 eps eps))) (.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) (.f64 eps eps)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) #s(literal 2 binary64)) (.f64 eps (.f64 eps (.f64 eps eps)))) (-.f64 (/.f64 (.f64 (.f64 eps eps) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64))) (.f64 eps eps)) (.f64 eps eps)))
(/.f64 (.f64 (.f64 eps eps) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (.f64 eps eps)))))
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(/.f64 (-.f64 (.f64 (.f64 eps eps) (+.f64 eps (tan.f64 eps))) (.f64 (+.f64 eps (tan.f64 eps)) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) (.f64 (+.f64 eps (tan.f64 eps)) (+.f64 eps (tan.f64 eps))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (*.f64 eps eps)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 eps (tan.f64 eps)))))
(pow.f64 (/.f64 (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps)) (-.f64 (.f64 eps (*.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 eps (tan.f64 eps)) (-.f64 (*.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64)))) #s(literal -1 binary64))
(.f64 (-.f64 (.f64 eps (.f64 eps eps)) (pow.f64 (tan.f64 eps) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (tan.f64 eps) (+.f64 eps (tan.f64 eps)) (.f64 eps eps))))
(.f64 (-.f64 (.f64 eps eps) (pow.f64 (tan.f64 eps) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 eps (tan.f64 eps))))
(*.f64 eps #s(literal -1/362880 binary64))
(*.f64 #s(literal -1/362880 binary64) eps)

simplify443.0ms (2.4%)

Memory

-27.8MiB live, 546.9MiB allocated

Algorithm

1×	egg-herbie

Rules

11 004×	`lower-fma.f64`
11 004×	`lower-fma.f32`
5 230×	`lower-+.f64`
5 230×	`lower-+.f32`
4 412×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	354	2545
1	1017	2479
2	3124	2425
0	8246	2283

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 178

Calls

Call 1

Inputs
(* 1/3 (pow eps 4))
(* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(- (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (/ (sin eps) eps)))))
(- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (- (cos (* -2 eps)) 1)) (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (/ (sin eps) eps)))))
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1/2 (/ (- (cos (* -2 eps)) 1) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))
(+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1/2 (- (cos (* -2 eps)) 1)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1/2 (- (cos (* -2 eps)) 1)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(pow eps 2)
(* 1/3 (pow eps 2))
(* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2))))
(* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
1
(+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))
(+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))
(+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))
1
(+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))
(+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))
(+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (/ 1/5040 (pow eps 2)) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* (pow eps 8) (- (+ (/ 1/5040 (pow eps 2)) (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* (pow eps 3) (cos eps)))) (+ 1/362880 (+ (* 1/362880 (/ (sin eps) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (* (pow eps 2) (pow (cos eps) 2))))))))
(* -1/362880 (pow eps 8))
(* (pow eps 8) (- (* -1/362880 (/ (sin eps) (* eps (cos eps)))) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(* (pow eps 8) (- (* -1 (/ (- (* -1 (/ (- (+ 1/5040 (/ (* (sin eps) (- 1/5040 (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2))))) (* eps (cos eps)))) (* 1/362880 (/ (pow (sin eps) 2) (pow (cos eps) 2)))) eps)) (* -1/362880 (/ (sin eps) (cos eps)))) eps)) 1/362880))
(* 1/6 (pow eps 3))
(* (pow eps 3) (+ 1/6 (* -1/120 (pow eps 2))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* (pow eps 3) (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(* -1/362880 (pow eps 9))
(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 9) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 9) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 9))
(* -1 (* (pow eps 9) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 9) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))
(* 1/6 eps)
(* eps (+ 1/6 (* -1/120 (pow eps 2))))
(* eps (+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120))))
(* eps (+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120))))
(* -1/362880 (pow eps 7))
(* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 7) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 7) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 7))
(* -1 (* (pow eps 7) (- 1/362880 (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (* 1/5040 (/ 1 (pow eps 2))))))
(* -1 (* (pow eps 7) (- (+ 1/362880 (/ 1/120 (pow eps 4))) (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))))))
1/6
(+ 1/6 (* -1/120 (pow eps 2)))
(+ 1/6 (* (pow eps 2) (- (* 1/5040 (pow eps 2)) 1/120)))
(+ 1/6 (* (pow eps 2) (- (* (pow eps 2) (+ 1/5040 (* -1/362880 (pow eps 2)))) 1/120)))
(* -1/362880 (pow eps 6))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* -1/362880 (pow eps 6))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) 1/362880))
(* (pow eps 6) (- (* 1/5040 (/ 1 (pow eps 2))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
(* (pow eps 6) (- (+ (* 1/5040 (/ 1 (pow eps 2))) (* 1/6 (/ 1 (pow eps 6)))) (+ 1/362880 (/ 1/120 (pow eps 4)))))
-1/2
(- (* 9/40 (pow eps 2)) 1/2)
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
(- (+ 1 (+ (* -1 (/ (+ (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* 1/2 (cos (* 2 eps))) (+ 1/2 (+ (* -1 (/ (pow (sin eps) 2) (cos eps))) (* -1 (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) (pow eps 3))) (* 1/2 (/ (cos (* 2 eps)) (pow eps 2))))) (+ (* -1 (/ (sin eps) (* eps (cos eps)))) (+ (* -1 (/ (pow (sin eps) 2) (* (pow eps 2) (cos eps)))) (+ (* -1 (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) (pow eps 2))) (+ (/ 1/2 (pow eps 2)) (/ (sin eps) eps))))))
1
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(+ 1 (* -1 (/ (- (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (- (* 1/2 (cos (neg (* -2 eps)))) 1/2) eps)))) (+ (/ (pow (sin eps) 2) (* eps (cos eps))) (/ (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2) eps))) eps)))
(+ 1 (* -1 (/ (+ (sin eps) (+ (* -1 (/ (sin eps) (cos eps))) (* -1 (/ (+ (* -1 (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2)))) (* -1 (/ (+ (* -1 (* (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) (- (* -1 (- (* 1/2 (cos (neg (* -2 eps)))) 1/2)) (+ (/ (pow (sin eps) 2) (cos eps)) (pow (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) 2))))) (/ (* (pow (sin eps) 2) (+ (sin eps) (* -1 (/ (sin eps) (cos eps))))) (cos eps))) eps))) eps)))) eps)))
(* 1/3 (pow eps 4))
(* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (* 2 eps)) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(pow eps 2)
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 2) (- (+ 1 (* 1/2 (/ (cos (neg (* -2 eps))) (pow eps 2)))) (* 1/2 (/ 1 (pow eps 2)))))
(* -1 (pow eps 2))
(* (pow eps 2) (- (* 1/3 (pow eps 2)) 1))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* -2/45 (pow eps 2)))) 1))
(* (pow eps 2) (- (* (pow eps 2) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45)))) 1))
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (* 2 eps))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
(- (* 1/2 (cos (neg (* -2 eps)))) 1/2)
1
(+ 1 (* -2 (pow eps 2)))
(+ 1 (* (pow eps 2) (- (* 2/3 (pow eps 2)) 2)))
(+ 1 (* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* -4/45 (pow eps 2)))) 2)))
(cos (* 2 eps))
(cos (* 2 eps))
(cos (* 2 eps))
(cos (* 2 eps))
(cos (neg (* -2 eps)))
(cos (neg (* -2 eps)))
(cos (neg (* -2 eps)))
(cos (neg (* -2 eps)))
(* -2 (pow eps 2))
(* (pow eps 2) (- (* 2/3 (pow eps 2)) 2))
(* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* -4/45 (pow eps 2)))) 2))
(* (pow eps 2) (- (* (pow eps 2) (+ 2/3 (* (pow eps 2) (- (* 2/315 (pow eps 2)) 4/45)))) 2))
(- (cos (* -2 eps)) 1)
(- (cos (* -2 eps)) 1)
(- (cos (* -2 eps)) 1)
(- (cos (* -2 eps)) 1)
(- (cos (* -2 eps)) 1)
(- (cos (* -2 eps)) 1)
(- (cos (* -2 eps)) 1)
(- (cos (* -2 eps)) 1)
(* -1/3 (pow eps 3))
(* (pow eps 3) (- (* -2/15 (pow eps 2)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* -17/315 (pow eps 2)) 2/15)) 1/3))
(* (pow eps 3) (- (* (pow eps 2) (- (* (pow eps 2) (- (* -62/2835 (pow eps 2)) 17/315)) 2/15)) 1/3))
eps
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
(* eps (+ 1 (* -1 (/ (sin eps) (* eps (cos eps))))))
eps
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1 (* eps (- (/ (sin eps) (* eps (cos eps))) 1)))
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)
(* -1/362880 eps)

Outputs
(* 1/3 (pow eps 4))
(.f64 #s(literal 1/3 binary64) (.f64 (.f64 eps eps) (.f64 eps eps)))
(* (pow eps 4) (+ 1/3 (* -2/45 (pow eps 2))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 #s(literal -2/45 binary64) (*.f64 eps eps) #s(literal 1/3 binary64)))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* 1/315 (pow eps 2)) 2/45))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 eps (.f64 eps (fma.f64 (.f64 eps eps) #s(literal 1/315 binary64) #s(literal -2/45 binary64))) #s(literal 1/3 binary64)))
(* (pow eps 4) (+ 1/3 (* (pow eps 2) (- (* (pow eps 2) (+ 1/315 (* -2/14175 (pow eps 2)))) 2/45))))
(.f64 (.f64 (.f64 eps eps) (.f64 eps eps)) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps (fma.f64 (*.f64 eps eps) #s(literal -2/14175 binary64) #s(literal 1/315 binary64))) #s(literal -2/45 binary64))) #s(literal 1/3 binary64)))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(.f64 eps (fma.f64 eps (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (*.f64 eps eps)) eps))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(.f64 eps (fma.f64 eps (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (*.f64 eps eps)) eps))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(.f64 eps (fma.f64 eps (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (*.f64 eps eps)) eps))
(pow eps 2)
(*.f64 eps eps)
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(.f64 eps (fma.f64 eps (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (*.f64 eps eps)) eps))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(.f64 eps (fma.f64 eps (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (*.f64 eps eps)) eps))
(* (pow eps 2) (+ 1 (* 1/2 (/ (- (cos (* -2 eps)) 1) (pow eps 2)))))
(.f64 eps (fma.f64 eps (/.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1/2 binary64)) (*.f64 eps eps)) eps))
-1/2
#s(literal -1/2 binary64)
(- (* 9/40 (pow eps 2)) 1/2)
(fma.f64 eps (*.f64 eps #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* -27/2800 (pow eps 2)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -27/2800 binary64) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(- (* (pow eps 2) (+ 9/40 (* (pow eps 2) (- (* 27/112000 (pow eps 2)) 27/2800)))) 1/2)
(fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (+ (sin eps) (* -1 (/ (sin eps) (cos eps)))) eps)))
(-.f64 #s(literal 1 binary64) (*.f64 (+.f64 (/.f64 #s(literal -1 binary64) (cos.f64 eps)) #s(literal 1 binary64)) (/.f64 (sin.f64 eps) eps)))
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(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))
(* -1/362880 eps)
(*.f64 eps #s(literal -1/362880 binary64))

eval117.0ms (0.6%)

Memory: -2.5MiB live, 145.0MiB allocated
Compiler: Compiled 31 156 to 2 415 computations (92.2% saved)

prune96.0ms (0.5%)

Memory

-5.0MiB live, 155.7MiB allocated

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	890	1	891
Fresh	0	0	0
Picked	0	3	3
Done	0	6	6
Total	890	10	900

Accuracy

100.0%

Counts

900 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.8%	(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
✓	99.7%	(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
✓	99.8%	(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
✓	1.0%	(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
✓	1.6%	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
✓	1.7%	(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
✓	1.0%	(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
	1.7%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (tan.f64 eps)) (.f64 eps (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps)))))
✓	99.0%	#s(literal -1/2 binary64)

Compiler

Compiled 550 to 199 computations (63.8% saved)

regimes10.0ms (0.1%)

Memory

18.3MiB live, 18.3MiB allocated

Counts

17 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(/.f64 (fma.f64 (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) (.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (*.f64 eps eps) #s(literal 27/112000 binary64) #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal 1/2 binary64)))
(/.f64 (.f64 (.f64 eps (.f64 eps eps)) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) #s(literal -1/362880 binary64) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64))) (-.f64 eps (tan.f64 eps)))
(/.f64 (.f64 (.f64 (fma.f64 (.f64 eps eps) (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64)) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) eps) (.f64 eps eps)) (-.f64 eps (tan.f64 eps)))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 eps (tan.f64 eps)) (.f64 eps (.f64 (fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (.f64 eps #s(literal -1/362880 binary64)) #s(literal 1/5040 binary64))) #s(literal -1/120 binary64)) #s(literal 1/6 binary64)) (.f64 eps eps)))))
(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))
(/.f64 (fma.f64 eps eps (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 (cos.f64 (+.f64 eps eps)) #s(literal 1/2 binary64) (fma.f64 eps eps #s(literal -1/2 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 eps eps (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps))))) (.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(.f64 (/.f64 (+.f64 (-.f64 (.f64 eps eps) #s(literal 1/2 binary64)) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 eps eps)))) (-.f64 eps (tan.f64 eps))) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))))
(/.f64 (.f64 (.f64 eps eps) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps eps)) (+.f64 (cos.f64 (.f64 eps #s(literal -2 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64))) (*.f64 (-.f64 eps (tan.f64 eps)) (+.f64 eps (sin.f64 eps))))
(/.f64 (fma.f64 (.f64 eps eps) (/.f64 #s(literal 1 binary64) (+.f64 eps (sin.f64 eps))) (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (+.f64 eps eps))) (.f64 (+.f64 eps (sin.f64 eps)) #s(literal 2 binary64))))) (-.f64 eps (tan.f64 eps)))

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Calls

2 calls:

5.0ms	eps
4.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.9%	1	`eps`
99.9%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes4.0ms (0%)

Memory

7.5MiB live, 7.5MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.8%	1	`eps`
99.8%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes3.0ms (0%)

Memory

6.7MiB live, 6.7MiB allocated

Counts

3 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
(fma.f64 (*.f64 eps eps) #s(literal 9/40 binary64) #s(literal -1/2 binary64))

Outputs
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))

Calls

2 calls:

2.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.7%	1	`eps`
99.7%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

regimes5.0ms (0%)

Memory

-37.1MiB live, 4.5MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal -1/2 binary64)

Outputs
#s(literal -1/2 binary64)

Calls

2 calls:

3.0ms	eps
1.0ms	(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))

Results

Accuracy	Segments	Branch
99.0%	1	`eps`
99.0%	1	`(/.f64 (-.f64 eps (sin.f64 eps)) (-.f64 eps (tan.f64 eps)))`

Compiler

Compiled 12 to 7 computations (41.7% saved)

simplify6.0ms (0%)

Memory

5.8MiB live, 5.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	34
1	18	34

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

Outputs
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps (fma.f64 eps (*.f64 eps #s(literal 27/112000 binary64)) #s(literal -27/2800 binary64))) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 (.f64 eps eps) (fma.f64 eps (.f64 eps #s(literal -27/2800 binary64)) #s(literal 9/40 binary64)) #s(literal -1/2 binary64))
(fma.f64 #s(literal 9/40 binary64) (*.f64 eps eps) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)

soundness358.0ms (1.9%)

Memory

-3.8MiB live, 197.9MiB allocated

Rules

12 288×	`lower-fma.f64`
12 288×	`lower-fma.f32`
6 122×	`lower-*.f64`
6 122×	`lower-*.f32`
1 424×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	148	561
1	422	524
2	1321	499
3	5650	444
0	8479	418

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 73 to 41 computations (43.8% saved)

preprocess50.0ms (0.3%)

Memory: 25.9MiB live, 102.8MiB allocated
Remove: (abs eps)
Compiler: Compiled 216 to 120 computations (44.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22

analyze369.0ms (2%)

sample9.4s (50.5%)

preprocess57.0ms (0.3%)

explain568.0ms (3.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify26.0ms (0.1%)

localize318.0ms (1.7%)

series5.0ms (0%)

rewrite329.0ms (1.8%)

simplify369.0ms (2%)

eval72.0ms (0.4%)

prune133.0ms (0.7%)

simplify258.0ms (1.4%)

localize758.0ms (4.1%)

series30.0ms (0.2%)

rewrite153.0ms (0.8%)

simplify396.0ms (2.1%)

eval269.0ms (1.4%)

prune76.0ms (0.4%)

simplify406.0ms (2.2%)

localize668.0ms (3.6%)

series21.0ms (0.1%)

rewrite379.0ms (2%)

simplify602.0ms (3.2%)

eval339.0ms (1.8%)

prune271.0ms (1.5%)

simplify262.0ms (1.4%)

localize621.0ms (3.3%)

series18.0ms (0.1%)

rewrite340.0ms (1.8%)

simplify443.0ms (2.4%)

eval117.0ms (0.6%)

prune96.0ms (0.5%)

regimes10.0ms (0.1%)

regimes4.0ms (0%)

regimes3.0ms (0%)

regimes5.0ms (0%)

simplify6.0ms (0%)

soundness358.0ms (1.9%)

preprocess50.0ms (0.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	27
1	29	23
2	78	18
3	239	18
4	501	18
5	688	18
6	705	18
7	743	18
8	772	18
0	6	9
0	11	9
1	18	9
2	28	9
3	45	9
4	79	9
5	151	9
6	326	9
7	624	9
8	928	9
9	943	9
10	944	9
0	944	9

Iter	Nodes	Cost
0	6	22
0	11	22
1	18	22
2	28	22
3	45	22
4	79	22
5	151	22
6	326	22
7	624	22
8	928	22
9	943	22
10	944	22
0	944	22