Metrics for tanhf (example 3.4)

analyze117.0ms (1.8%)

Memory

21.5MiB live, 138.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
25%	25%	75%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.8s (27.9%)

Memory

28.7MiB live, 1 781.4MiB allocated

Samples

682.0ms	2 290×	2	valid
455.0ms	4 159×	0	valid
190.0ms	535×	3	valid
186.0ms	1 264×	1	valid
9.0ms	8×	4	valid

Precisions

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

ival-cos: 719.0ms (55.9% of total)

ival-sin: 188.0ms (14.6% of total)

ival-div: 172.0ms (13.4% of total)

adjust: 109.0ms (8.5% of total)

ival-sub: 84.0ms (6.5% of total)

ival-true: 6.0ms (0.5% of total)

exact: 6.0ms (0.5% of total)

ival-assert: 3.0ms (0.2% of total)

Bogosity

preprocess90.0ms (1.4%)

Memory

-11.7MiB live, 26.2MiB allocated

Algorithm

1×	egg-herbie

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
98×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(neg.f64 (tan.f64 (*.f64 x #s(literal -1/2 binary64))))

Symmetry

(negabs x)

explain153.0ms (2.4%)

Memory

22.3MiB live, 155.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
73	0	-	2	(2.4851955992015e-161)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
67	2	(6.586462125114374e+89)	2	(8.256398474500535e+119)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	71	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	71
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	67	7

Confusion

	Predicted +	Predicted -
+	137	2
-	1	116

Precision

0.9927536231884058

Recall

0.9856115107913669

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	137	2	0
-	1	5	111

Precision?

0.9586206896551724

Recall?

1.0

Freqs

test

number	freq
0	118
1	138

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

55.0ms	146×	2	valid
27.0ms	254×	0	valid
13.0ms	38×	3	valid
10.0ms	74×	1	valid

Compiler

Compiled 54 to 28 computations (48.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 88.0ms

ival-cos: 42.0ms (47.7% of total)

ival-sin: 25.0ms (28.4% of total)

adjust: 7.0ms (8% of total)

ival-sub: 7.0ms (8% of total)

ival-div: 6.0ms (6.8% of total)

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

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

exact: 0.0ms (0% of total)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune45.0ms (0.7%)

Memory

-35.6MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify30.0ms (0.5%)

Memory

-3.6MiB live, 39.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	6848	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Rules

204×	`lower-fma.f64`
204×	`lower-fma.f32`
140×	`lower-*.f64`
140×	`lower-*.f32`
82×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

Outputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(neg.f64 (tan.f64 (*.f64 x #s(literal -1/2 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(cos.f64 x)
x
(sin.f64 x)

localize57.0ms (0.9%)

Memory

9.0MiB live, 85.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	78.4%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	73.4%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Samples

21.0ms	73×	2	valid
14.0ms	127×	0	valid
6.0ms	19×	3	valid
6.0ms	37×	1	valid

Compiler

Compiled 19 to 8 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-cos: 21.0ms (58.4% of total)

ival-sin: 5.0ms (13.9% of total)

adjust: 3.0ms (8.3% of total)

ival-div: 3.0ms (8.3% of total)

ival-sub: 3.0ms (8.3% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0%)

Memory

4.5MiB live, 4.5MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))>
#<alt (-.f64 #s(literal 1 binary64) (cos.f64 x))>
#<alt (cos.f64 x)>
#<alt (sin.f64 x)>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	-inf	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	0	(cos x)
0.0ms	x	@	0	(/ (- 1 (cos x)) (sin x))
0.0ms	x	@	0	(- 1 (cos x))

simplify446.0ms (6.8%)

Memory

23.4MiB live, 537.3MiB allocated

Algorithm

1×	egg-herbie

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
3 796×	`lower-*.f64`
3 796×	`lower-*.f32`
3 232×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	79	286
1	224	286
2	555	280
3	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	256

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 47

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal -1/24 binary64) #s(literal 1/2 binary64))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal -1/40320 binary64)) #s(literal 1/720 binary64)) #s(literal -1/24 binary64)) #s(literal 1/2 binary64)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal -1/720 binary64)) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)) #s(literal 1 binary64))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(fma.f64 x (.f64 (.f64 x x) #s(literal -1/6 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/120 binary64)) #s(literal -1/6 binary64)) (.f64 x (*.f64 x x)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(fma.f64 (fma.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal -1/5040 binary64)) #s(literal 1/120 binary64))) #s(literal -1/6 binary64)) (.f64 x (.f64 x x)) x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)

rewrite281.0ms (4.3%)

Memory

24.3MiB live, 490.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 606×	`lower-*.f64`
4 606×	`lower-*.f32`
3 722×	`lower-/.f32`
3 720×	`lower-/.f64`
2 028×	`lower--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Counts

4 → 615

Calls

Call 1

Inputs
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos.f64 x)
(sin.f64 x)

Outputs
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))) #s(literal -1 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)) (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+.f64 (.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (*.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal 1 binary64)))
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(.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 3 binary64)))) (fma.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (-.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(*.f64 (pow.f64 (/.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(exp.f64 (log.f64 (cos.f64 x)))
(exp.f64 (*.f64 (log.f64 (cos.f64 x)) #s(literal 1 binary64)))
(cos.f64 x)
(-.f64 #s(literal 0 binary64) (neg.f64 (cos.f64 x)))
(neg.f64 (neg.f64 (cos.f64 x)))
(pow.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (cos.f64 x)))
(*.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (cos.f64 x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (sin.f64 x)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sin.f64 x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x)))
(sin.f64 x)
(neg.f64 (neg.f64 (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(/.f64 (sin.f64 x) #s(literal 1 binary64))
(/.f64 (neg.f64 (sin.f64 x)) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (sin.f64 x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sin.f64 x)))
(/.f64 (+.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1 binary64)) (neg.f64 (sin.f64 x)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal -1 binary64)) (.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 (sin.f64 x))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x))) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64)) (neg.f64 (sin.f64 x)))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))) (neg.f64 (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal -1 binary64))) (sin.f64 x))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (+.f64 #s(literal 3/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (neg.f64 (sin.f64 x)))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))) (neg.f64 (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(pow.f64 (sin.f64 x) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (sin.f64 x))
(*.f64 (sin.f64 x) #s(literal 1 binary64))
(.f64 (sin.f64 x) (.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (sin.f64 x))))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))))
(.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sin.f64 x)))
(.f64 (pow.f64 (/.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 6 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)) #s(literal 1/2 binary64)) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) #s(literal 1 binary64))))
(.f64 (pow.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 3/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))

eval134.0ms (2.1%)

Memory: -29.8MiB live, 138.6MiB allocated
Compiler: Compiled 14 403 to 1 633 computations (88.7% saved)

prune78.0ms (1.2%)

Memory

4.2MiB live, 166.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	657	5	662
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	658	5	663

Accuracy

100.0%

Counts

663 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.1%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
▶	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	51.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	52.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
▶	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 72 to 52 computations (27.8% saved)

simplify45.0ms (0.7%)

Memory

3.4MiB live, 44.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	6464	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(*.f64 x #s(literal 1/24 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Rules

580×	`lower-fma.f32`
574×	`lower-fma.f64`
284×	`lower-*.f32`
270×	`lower-*.f64`
256×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal -1/2 binary64)

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
x
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(.f64 x (fma.f64 #s(literal 1/24 binary64) (.f64 x x) #s(literal 1/2 binary64)))
x
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
x
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
#s(literal 1/2 binary64)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
#s(literal 1 binary64)
#s(literal 1 binary64)
#s(literal -1/2 binary64)

localize137.0ms (2.1%)

Memory

-6.0MiB live, 191.0MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	51.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.5%	(*.f64 x #s(literal 1/24 binary64))
✓	accuracy	52.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Samples

44.0ms	73×	2	valid
34.0ms	127×	0	valid
13.0ms	19×	3	valid
13.0ms	37×	1	valid

Compiler

Compiled 109 to 27 computations (75.2% saved)

Precisions

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

ival-cos: 22.0ms (26.4% of total)

ival-mult: 17.0ms (20.4% of total)

adjust: 11.0ms (13.2% of total)

const: 8.0ms (9.6% of total)

ival-div: 5.0ms (6% of total)

ival-tan: 5.0ms (6% of total)

ival-add: 5.0ms (6% of total)

ival-sin: 5.0ms (6% of total)

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

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

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.1%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

15 → 168

Calls

Call 1

Inputs
#<alt (tan.f64 (*.f64 x #s(literal 1/2 binary64)))>
#<alt (*.f64 x #s(literal 1/2 binary64))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))>
#<alt (*.f64 #s(literal 1/2 binary64) x)>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))>
#<alt (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x #s(literal 1/24 binary64))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))>
#<alt (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))>
#<alt (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))>
#<alt (*.f64 x x)>
#<alt (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))>
#<alt (*.f64 x #s(literal 1/240 binary64))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 3))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 (pow x 2))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/24 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))>
#<alt (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))>
#<alt (* 1/240 (pow x 4))>
#<alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 4))>
#<alt (* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>

Calls

42 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2)
1.0ms	x	@	inf	(* x 1/2)
1.0ms	x	@	inf	(* x (+ (* x (* x 1/24)) 1/2))
0.0ms	x	@	inf	(tan (* x 1/2))
0.0ms	x	@	inf	(* x (+ (* (* x x) (+ (* x (* x 1/240)) 1/24)) 1/2))

simplify367.0ms (5.6%)

Memory

-14.6MiB live, 397.9MiB allocated

Algorithm

1×	egg-herbie

Rules

14 916×	`lower-fma.f64`
14 916×	`lower-fma.f32`
3 880×	`lower-*.f64`
3 880×	`lower-*.f32`
2 216×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	1034
1	192	1034
2	479	1034
3	1125	1034
4	2283	1034
5	5525	1034
0	8283	953

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 3))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 (pow x 2))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 4))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/24 (pow x 3))
(.f64 x (.f64 x (*.f64 x #s(literal 1/24 binary64))))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 3) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/24 (pow x 2))
(.f64 x (.f64 x #s(literal 1/24 binary64)))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 2) (+ 1/24 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/24 x)
(*.f64 x #s(literal 1/24 binary64))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 17/40320 binary64)) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/240 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* 1/240 (pow x 5))
(.f64 x (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 (.f64 x x) (.f64 x (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* 1/24 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/240 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* 1/240 (pow x 4))
(.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/240 binary64)))
(* (pow x 4) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(* (pow x 4) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))

rewrite437.0ms (6.7%)

Memory

10.8MiB live, 530.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 674×	`lower-fma.f32`
8 668×	`lower-fma.f64`
5 812×	`lower-*.f32`
5 798×	`lower-*.f64`
3 982×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	114
0	40	103
1	148	103
2	917	103
0	8416	103

Stop Event

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

Counts

15 → 571

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1/2 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 #s(literal 1/2 binary64) x)
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x #s(literal 1/24 binary64))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))
(*.f64 x x)
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/240 binary64))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (tan.f64 (.f64 x #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal -1 binary64) (tan.f64 x)))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (tan.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))))
(+.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (*.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) #s(literal 1 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (tan.f64 x)) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(+.f64 (*.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (neg.f64 (cos.f64 x))) (/.f64 #s(literal 1 binary64) (sin.f64 x)))
(-.f64 #s(literal 0 binary64) (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (tan.f64 x)))
(-.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))) (/.f64 (.f64 (sin.f64 x) (cos.f64 x)) (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x))))))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)) (/.f64 (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))) (sin.f64 x)))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)) (/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sin.f64 x))) (neg.f64 (tan.f64 (*.f64 x #s(literal 1/2 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (.f64 (sin.f64 x) (fma.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (+.f64 x x)))) (*.f64 (sin.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
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(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)))))
(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64))) (neg.f64 (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64))))))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64))) (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64)))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64))) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/240 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64)) #s(literal 1/2641807540224 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) (-.f64 #s(literal 1/191102976 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/191102976000 binary64)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal -1/13824 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/5760 binary64))))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (+.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/33177600 binary64)))) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) #s(literal -1/331776 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal 1/576 binary64)) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/5760 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)))) (neg.f64 (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/240 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))) (.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64)) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64)) #s(literal 1/2641807540224 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) (-.f64 #s(literal 1/191102976 binary64) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/191102976000 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal -1/13824 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (+.f64 #s(literal 1/331776 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/33177600 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) #s(literal -1/331776 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal 1/576 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/5760 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64))))))
(.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (*.f64 x x) #s(literal 1/5760 binary64)))))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (*.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/240 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (-.f64 (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64))) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/57600 binary64))))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal 1/13824 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (-.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))) (+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))) (+.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (.f64 (.f64 x x) #s(literal 1/5760 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) #s(literal -1/576 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)) #s(literal -1/13824 binary64))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/57600 binary64) (+.f64 #s(literal 1/576 binary64) (.f64 (.f64 x x) #s(literal 1/5760 binary64)))))

eval101.0ms (1.6%)

Memory: -11.1MiB live, 209.5MiB allocated
Compiler: Compiled 20 298 to 1 627 computations (92% saved)

prune114.0ms (1.7%)

Memory

14.9MiB live, 180.3MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	737	2	739
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	738	6	744

Accuracy

100.0%

Counts

744 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	51.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	51.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	52.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
▶	8.1%	#s(literal 1 binary64)

Compiler

Compiled 50 to 34 computations (32% saved)

simplify43.0ms (0.7%)

Memory

0.6MiB live, 38.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x #s(literal 1/240 binary64))
✓	cost-diff	0	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	cost-diff	0	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	cost-diff	320	(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))

Rules

580×	`lower-fma.f32`
576×	`lower-fma.f64`
284×	`lower-*.f32`
276×	`lower-*.f64`
230×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	63
0	24	54
1	46	54
2	70	54
3	159	54
4	295	54
5	338	54
6	371	54
7	445	54
8	567	54
9	773	54
10	815	54
11	818	54
12	826	54
13	832	54
14	836	54
15	843	54
16	923	54
17	1008	54
18	1012	54
0	1012	54

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
x
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)

Outputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64))))
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
(.f64 x (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
x
(*.f64 x #s(literal 1/240 binary64))
#s(literal 1/240 binary64)
#s(literal 1/24 binary64)
(.f64 x (.f64 x x))
(*.f64 x x)
(*.f64 x #s(literal 1/2 binary64))
#s(literal 1/2 binary64)

localize112.0ms (1.7%)

Memory

-3.1MiB live, 161.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
✓	accuracy	99.9%	(*.f64 x #s(literal 1/240 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	51.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))

Samples

39.0ms	73×	2	valid
35.0ms	127×	0	valid
10.0ms	19×	3	valid
9.0ms	37×	1	valid

Compiler

Compiled 52 to 19 computations (63.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-cos: 22.0ms (29.6% of total)

const: 13.0ms (17.5% of total)

ival-sin: 11.0ms (14.8% of total)

ival-mult: 9.0ms (12.1% of total)

adjust: 7.0ms (9.4% of total)

ival-div: 5.0ms (6.7% of total)

ival-add: 4.0ms (5.4% of total)

ival-sub: 3.0ms (4% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))>
#<alt #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))>
#<alt (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))>
#<alt (*.f64 x #s(literal 1/240 binary64))>
#<alt (.f64 x (.f64 x x))>

Outputs
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))>
#<alt (* 1/240 (pow x 5))>
#<alt (* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt (/ (- 1 (cos x)) (sin x))>
#<alt 1/24>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (+ 1/24 (* 1/240 (pow x 2)))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 (pow x 2))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (* 1/240 x)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ (* (+ (* x (* x 1/240)) 1/24) (* x (* x x))) (* x 1/2))
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	-inf	(+ (* (+ (* x (* x 1/240)) 1/24) (* x (* x x))) (* x 1/2))
0.0ms	x	@	0	(* x (* x x))
0.0ms	x	@	0	(+ (* (+ (* x (* x 1/240)) 1/24) (* x (* x x))) (* x 1/2))

simplify281.0ms (4.3%)

Memory

17.8MiB live, 397.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 762×	`lower-fma.f64`
9 762×	`lower-fma.f32`
3 786×	`lower-*.f64`
3 786×	`lower-*.f32`
1 274×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	360
1	155	360
2	376	360
3	871	360
4	1592	360
5	3468	360
6	7519	360
0	8099	330

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(* 1/240 (pow x 5))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
(/ (- 1 (cos x)) (sin x))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 (pow x 2))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(* 1/240 x)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)

Outputs
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* 1/240 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* (pow x 5) (+ 1/240 (+ (/ 1/2 (pow x 4)) (* 1/24 (/ 1 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* 1/240 (pow x 5))
(.f64 (.f64 x x) (.f64 x (.f64 (*.f64 x x) #s(literal 1/240 binary64))))
(* (pow x 5) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(.f64 x (.f64 x (.f64 x (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)))))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* -1 (* (pow x 5) (- (* -1 (/ (+ 1/24 (* 1/2 (/ 1 (pow x 2)))) (pow x 2))) 1/240)))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (fma.f64 x (.f64 x (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))) #s(literal 1/2 binary64)))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal 17/40320 binary64) #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ (- 1 (cos x)) (sin x))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
1/24
#s(literal 1/24 binary64)
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(+ 1/24 (* 1/240 (pow x 2)))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/240 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* (pow x 2) (+ 1/240 (* 1/24 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(* 1/240 x)
(*.f64 x #s(literal 1/240 binary64))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))

rewrite700.0ms (10.8%)

Memory

-43.6MiB live, 457.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 424×	`lower-fma.f32`
7 420×	`lower-fma.f64`
5 166×	`lower-*.f32`
5 158×	`lower-*.f64`
3 082×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	52
0	24	43
1	91	43
2	632	43
3	7449	43
0	8105	43

Stop Event

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

Counts

5 → 207

Calls

Call 1

Inputs
(fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64))
(*.f64 x #s(literal 1/240 binary64))
(.f64 x (.f64 x x))

Outputs
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))))) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))))) (.f64 x (fma.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (neg.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (fma.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal -1/2 binary64))))))
(+.f64 (.f64 x (.f64 x (.f64 x (.f64 #s(literal 1/240 binary64) (.f64 x x))))) (fma.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))) (fma.f64 x (.f64 x (.f64 x (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (.f64 x #s(literal 1/2 binary64))))
(+.f64 (fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x (.f64 #s(literal 1/240 binary64) (.f64 x x)))))) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64))))
(+.f64 (fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x (.f64 x (.f64 x (.f64 #s(literal 1/240 binary64) (.f64 x x))))))
(-.f64 (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))))) (.f64 x (fma.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))) (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (fma.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/4 binary64))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))))))) (/.f64 (.f64 x (.f64 (.f64 x x) (.f64 x (.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))))))) (.f64 x (-.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))))))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64))))))
(fma.f64 x (.f64 x (.f64 x (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (fma.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 x (.f64 x (.f64 x (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))) (.f64 x #s(literal 1/2 binary64)))
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)) (fma.f64 x (.f64 x (.f64 x (.f64 #s(literal 1/240 binary64) (.f64 x x)))) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 #s(literal 1/240 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x x))) (fma.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64))))
(fma.f64 (.f64 x #s(literal 1/240 binary64)) (.f64 x (.f64 x (.f64 x x))) (fma.f64 x (.f64 (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x #s(literal 1/2 binary64))))
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(/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64))) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))) (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64)))
(/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64)) #s(literal 1/2641807540224 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)) (-.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal 1/191102976 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/191102976000 binary64)))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal -1/13824 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/33177600 binary64) #s(literal 1/331776 binary64)))))
(/.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))))) (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/240 binary64))))
(/.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) #s(literal -1/331776 binary64)) (.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/57600 binary64))) #s(literal 1/576 binary64))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)) #s(literal 1/576 binary64))) (.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)) #s(literal 1 binary64)) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64)) #s(literal 1/2641807540224 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal 1/191102976 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/191102976000 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal -1/13824 binary64)) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/33177600 binary64) #s(literal 1/331776 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) #s(literal -1/331776 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/57600 binary64))) #s(literal 1/576 binary64)) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64)))) (neg.f64 (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)))) (neg.f64 (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))))) (neg.f64 (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/240 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (fma.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))) (.f64 (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))))) (fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64))) (/.f64 #s(literal 1/576 binary64) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal -1/24 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64)))) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64)) #s(literal 1/2641807540224 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)))) (-.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal 1/191102976 binary64)) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) #s(literal 1/191102976000 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)))) (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal -1/13824 binary64)))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) #s(literal -1/191102976 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64)))) (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/33177600 binary64) #s(literal 1/331776 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64) #s(literal -1/331776 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64)))) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/57600 binary64))) #s(literal 1/576 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64))))
(.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64))) (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (*.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64)))
(.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (.f64 x x) #s(literal -1/240 binary64) #s(literal 1/24 binary64))) (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (*.f64 x x))) #s(literal -1/576 binary64)))
(.f64 (-.f64 #s(literal 1/576 binary64) (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal -1/240 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)) (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64))) (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/191102976000000 binary64) (.f64 (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)) (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)))))) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal -1/5760 binary64) #s(literal 1/576 binary64)) (.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 1/3317760000 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal 1/13824 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/57600 binary64)) #s(literal 1/5760 binary64)) #s(literal 1/576 binary64)) (+.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)) (.f64 x (.f64 x #s(literal 1/5760 binary64)))))) (+.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)) (.f64 x (.f64 x #s(literal 1/5760 binary64)))))
(.f64 (/.f64 (fma.f64 #s(literal 1/57600 binary64) (.f64 x (.f64 x (.f64 x x))) #s(literal -1/576 binary64)) (fma.f64 (.f64 x x) (.f64 x (.f64 (.f64 x (.f64 x x)) #s(literal 1/13824000 binary64))) #s(literal -1/13824 binary64))) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/57600 binary64))) (fma.f64 x (*.f64 x #s(literal 1/5760 binary64)) #s(literal 1/576 binary64))))
(*.f64 x #s(literal 1/240 binary64))
(*.f64 #s(literal 1/240 binary64) x)
(exp.f64 (*.f64 #s(literal 3 binary64) (log.f64 x)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))

eval34.0ms (0.5%)

Memory: 32.5MiB live, 69.2MiB allocated
Compiler: Compiled 10 655 to 667 computations (93.7% saved)

prune32.0ms (0.5%)

Memory

-19.8MiB live, 60.8MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	267	6	273

Accuracy

100.0%

Counts

273 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	51.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
✓	51.9%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	52.0%	#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
✓	52.4%	#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
✓	8.1%	#s(literal 1 binary64)

Compiler

Compiled 105 to 58 computations (44.8% saved)

regimes7.0ms (0.1%)

Memory

13.3MiB live, 13.3MiB allocated

Counts

8 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))

Calls

2 calls:

3.0ms	x
3.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Memory

-26.4MiB live, 13.1MiB allocated

Counts

6 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
(pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64))))
#s(literal 1 binary64)

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
56.3%	2	`x`
56.1%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Memory

5.9MiB live, 5.9MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(literal 1 binary64)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64))))
#s(literal 1 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
56.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Memory

5.6MiB live, 5.6MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

#s(literal 1 binary64)

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

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
56.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
56.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Memory

7.3MiB live, 7.3MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1 binary64)

Outputs
#s(literal 1 binary64)

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
8.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
8.1%	1	`x`

Compiler

Compiled 10 to 7 computations (30% saved)

bsearch18.0ms (0.3%)

Memory

-6.0MiB live, 33.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
17.0ms	0.0017575237548262792	6.681927855507822

Samples

11.0ms

128×

valid

Compiler

Compiled 171 to 122 computations (28.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-cos: 3.0ms (35.7% of total)

ival-sin: 3.0ms (35.7% of total)

ival-sub: 1.0ms (11.9% of total)

ival-div: 1.0ms (11.9% of total)

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

exact: 0.0ms (0% of total)

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

bsearch1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0017575237548262792	6.681927855507822

Compiler

Compiled 155 to 114 computations (26.5% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0017575237548262792	6.681927855507822

Compiler

Compiled 115 to 90 computations (21.7% saved)

bsearch1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	0.0017575237548262792	6.681927855507822

Compiler

Compiled 75 to 66 computations (12% saved)

simplify6.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
2×	`1-exp_binary64`
2×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	96
1	41	96

Stop Event

1×

saturated

Calls

Call 1

Inputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
#s(literal 1 binary64)

Outputs
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (fma.f64 (fma.f64 x (.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) (.f64 x (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/240 binary64)) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (.f64 x (fma.f64 x (.f64 x #s(literal 1/24 binary64)) #s(literal 1/2 binary64)))) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x)) #s(literal 1 binary64))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) #s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))
#s(literal 1 binary64)

soundness740.0ms (11.4%)

Memory

-20.5MiB live, 457.7MiB allocated

Rules

19 148×	`lower-fma.f64`
19 148×	`lower-fma.f32`
8 674×	`lower-fma.f32`
8 668×	`lower-fma.f64`
5 812×	`lower-*.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	286
1	224	286
2	555	280
3	1656	280
4	3000	280
5	4243	280
6	4592	280
7	5323	280
8	6815	280
0	8390	256
0	25	114
0	40	103
1	148	103
2	917	103
0	8416	103
0	6	15
0	10	12
1	39	12
2	245	12
3	2355	11
0	8885	11

Stop Event

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

Compiler

Compiled 157 to 88 computations (43.9% saved)

preprocess63.0ms (1%)

Memory: -6.8MiB live, 156.5MiB allocated
Remove: (negabs x)
Compiler: Compiled 166 to 74 computations (55.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116

analyze117.0ms (1.8%)

sample1.8s (27.9%)

preprocess90.0ms (1.4%)

explain153.0ms (2.4%)

eval0.0ms (0%)

prune45.0ms (0.7%)

simplify30.0ms (0.5%)

localize57.0ms (0.9%)

series3.0ms (0%)

simplify446.0ms (6.8%)

rewrite281.0ms (4.3%)

eval134.0ms (2.1%)

prune78.0ms (1.2%)

simplify45.0ms (0.7%)

localize137.0ms (2.1%)

series10.0ms (0.1%)

simplify367.0ms (5.6%)

rewrite437.0ms (6.7%)

eval101.0ms (1.6%)

prune114.0ms (1.7%)

simplify43.0ms (0.7%)

localize112.0ms (1.7%)

series2.0ms (0%)

simplify281.0ms (4.3%)

rewrite700.0ms (10.8%)

eval34.0ms (0.5%)

prune32.0ms (0.5%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes3.0ms (0%)

bsearch18.0ms (0.3%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify6.0ms (0.1%)

soundness740.0ms (11.4%)

preprocess63.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	11
1	30	11
2	73	8
3	180	8
4	443	8
5	681	8
6	706	8
0	6	7
0	10	4
1	20	4
2	26	4
3	37	4
4	58	4
5	81	4
6	114	4
7	188	4
8	310	4
9	519	4
10	561	4
11	564	4
12	572	4
13	578	4
14	582	4
15	589	4
16	596	4
17	597	4
0	597	4

Iter	Nodes	Cost
0	6	17
0	10	14
1	20	14
2	26	14
3	37	14
4	58	14
5	81	14
6	114	14
7	188	14
8	310	14
9	519	14
10	561	14
11	564	14
12	572	14
13	578	14
14	582	14
15	589	14
16	596	14
17	597	14
0	597	14

Iter	Nodes	Cost
0	25	127
0	40	116
1	81	116
2	148	116
3	234	116
4	266	116
5	293	116
6	326	116
7	400	116
8	522	116
9	731	116
10	773	116
11	776	116
12	784	116
13	789	116
14	793	116
15	800	116
16	880	116
17	967	116
18	971	116
0	971	116