Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze110.0ms (2.5%)

Memory

20.6MiB live, 136.3MiB 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)

sample2.0s (46.5%)

Memory

14.5MiB live, 1 650.2MiB allocated

Samples

746.0ms	2 239×	2	valid
543.0ms	4 195×	0	valid
209.0ms	560×	3	valid
161.0ms	1 260×	1	valid
2.0ms	2×	4	valid

Precisions

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

ival-cos: 831.0ms (61.8% of total)

ival-sin: 186.0ms (13.8% of total)

adjust: 116.0ms (8.6% of total)

ival-div: 107.0ms (8% of total)

ival-sub: 91.0ms (6.8% of total)

ival-true: 6.0ms (0.4% of total)

exact: 5.0ms (0.4% of total)

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

Bogosity

explain225.0ms (5.2%)

Memory

16.1MiB live, 221.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
70	-	1	(2.8441913110461176e+240)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
65	-	4	(-4.784237852149848e-158)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(cos.f64 x)`
0	-	0	-	`(sin.f64 x)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	69	3
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	61	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	61

Confusion

	Predicted +	Predicted -
+	130	1
-	0	125

Precision

1.0

Recall

0.9923664122137404

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	130	1	0
-	0	2	123

Precision?

0.9849624060150376

Recall?

1.0

Freqs

test

number	freq
0	126
1	130

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

73.0ms	140×	2	valid
45.0ms	260×	0	valid
15.0ms	38×	3	valid
10.0ms	74×	1	valid

Compiler

Compiled 62 to 28 computations (54.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 120.0ms

ival-cos: 85.0ms (71% of total)

ival-sin: 13.0ms (10.9% of total)

adjust: 8.0ms (6.7% of total)

ival-div: 7.0ms (5.8% of total)

ival-sub: 6.0ms (5% of total)

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

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

exact: 0.0ms (0% of total)

preprocess42.0ms (1%)

Memory

7.8MiB live, 45.9MiB allocated

Algorithm

1×	egg-herbie

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 4 to 4 computations (0% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0.1%)

Memory

2.4MiB live, 2.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 x #s(literal 2 binary64))
cost-diff	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
0	6	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)

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

localize22.0ms (0.5%)

Memory

-17.5MiB live, 19.2MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(/.f64 x #s(literal 2 binary64))
accuracy	0	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Samples

14.0ms

256×

valid

Compiler

Compiled 20 to 10 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-tan: 5.0ms (67.9% of total)

ival-div: 2.0ms (27.2% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (tan.f64 (/.f64 x #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 x #s(literal 2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((tan (/ x 2)) (/ x 2))
1.0ms	x	@	inf	((tan (/ x 2)) (/ x 2))
1.0ms	x	@	0	((tan (/ x 2)) (/ x 2))

simplify15.0ms (0.3%)

Memory

17.9MiB live, 17.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	156
1	73	156
2	190	156
3	441	156
4	653	156
5	711	156
6	714	156
0	714	150

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 24

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))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 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)
(/ (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)

Outputs
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)

rewrite113.0ms (2.6%)

Memory

-2.2MiB live, 82.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	19	7
2	51	7
3	188	7
4	888	7
0	8099	7

Stop Event

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

Counts

2 → 432

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))

Outputs
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eval110.0ms (2.5%)

Memory: 14.4MiB live, 123.4MiB allocated
Compiler: Compiled 5 446 to 1 109 computations (79.6% saved)

prune19.0ms (0.4%)

Memory

-28.1MiB live, 20.1MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	452	4	456
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	453	4	457

Accuracy

100.0%

Counts

457 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
▶	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	51.1%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify7.0ms (0.2%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	110
0	31	110
1	46	110
2	73	110
3	126	110
4	206	110
5	216	110
6	221	110
0	221	110

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize108.0ms (2.5%)

Memory

5.2MiB live, 112.1MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x #s(literal 1/2 binary64))
accuracy	0	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
accuracy	0.04296875	(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
accuracy	0.060878759768442016	(fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64))
accuracy	0.06640625	(fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64))
accuracy	31.485103338399043	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 x x)
accuracy	0.0703125	(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
accuracy	0.09375	(fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64))
accuracy	31.471016495589602	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	31.295315347723506	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Samples

74.0ms

256×

valid

Compiler

Compiled 202 to 40 computations (80.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 58.0ms

ival-mult: 22.0ms (37.9% of total)

ival-tan: 14.0ms (24.1% of total)

const: 9.0ms (15.5% of total)

ival-div: 7.0ms (12% of total)

ival-add: 5.0ms (8.6% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

12.2MiB live, 12.2MiB allocated

Counts

12 → 144

Calls

Call 1

Inputs
#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (*.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 #s(literal 1/240 binary64) (*.f64 x x) #s(literal 1/24 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (tan.f64 (*.f64 x #s(literal 1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
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Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((tan (/ x 2)) (* 1/2 x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (/ x 2)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (tan (* x 1/2)) (* x 1/2))
2.0ms	x	@	-inf	((tan (/ x 2)) (* 1/2 x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (/ x 2)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (tan (* x 1/2)) (* x 1/2))
1.0ms	x	@	0	((tan (/ x 2)) (* 1/2 x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (/ x 2)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (tan (* x 1/2)) (* x 1/2))

Time

Variable

Point

Expression

2.0ms

inf

((tan (/ x 2)) (* 1/2 x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (/ x 2)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (tan (* x 1/2)) (* x 1/2))

2.0ms

-inf

((tan (/ x 2)) (* 1/2 x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (/ x 2)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (tan (* x 1/2)) (* x 1/2))

1.0ms

((tan (/ x 2)) (* 1/2 x) (tan (/ x 2)) (* (+ (* (* x x) 1/24) 1/2) x) (+ (* (* x x) 1/24) 1/2) (* x x) (tan (/ x 2)) (* (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) x) (+ (* (+ (* 1/240 (* x x)) 1/24) (* x x)) 1/2) (+ (* 1/240 (* x x)) 1/24) (tan (* x 1/2)) (* x 1/2))

simplify191.0ms (4.4%)

Memory

-5.4MiB live, 200.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	1082
1	177	1082
2	466	1082
3	1131	1082
4	2283	1082
5	5470	1082
0	8151	1001

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

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))))))))
(* 1/2 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))))))))
(* 1/2 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))))
1/2
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(+ 1/2 (* 1/24 (pow x 2)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 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))))))))
(* 1/2 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))))))
1/2
(+ 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)))))
1/24
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(+ 1/24 (* 1/240 (pow x 2)))
(* 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))))))))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 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)
(/ (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)))
(* 1/24 (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 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)))))
(pow x 2)
(pow x 2)
(pow x 2)
(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)))
(* 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 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 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)))))
(/ (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)
(/ (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)
(/ (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)))
(* 1/24 (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 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)))))
(pow x 2)
(pow x 2)
(pow x 2)
(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)))
(* 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)))
(* 1/240 (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 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)))))
(/ (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)

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

rewrite181.0ms (4.2%)

Memory

21.5MiB live, 211.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	96
0	31	96
1	101	96
2	558	96
3	5480	96
0	9126	96

Stop Event

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

Counts

12 → 444

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval105.0ms (2.4%)

Memory: -43.0MiB live, 127.0MiB allocated
Compiler: Compiled 15 788 to 1 854 computations (88.3% saved)

prune19.0ms (0.4%)

Memory

8.0MiB live, 46.8MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	622	2	624
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	622	6	628

Accuracy

100.0%

Counts

628 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
▶	50.8%	#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
▶	50.9%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
✓	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
✓	51.1%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 68 to 53 computations (22.1% saved)

simplify4.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 #s(literal 1/24 binary64) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
cost-diff	320	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
cost-diff	0	(/.f64 #s(literal 2 binary64) x)
cost-diff	0	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	58
0	22	54
1	34	52
2	51	52
3	55	52
0	55	50

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(literal 1 binary64)
(/.f64 #s(literal 2 binary64) x)
#s(literal 2 binary64)
x
#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
(*.f64 x x)
x
(*.f64 #s(literal 1/24 binary64) x)
#s(literal 1/24 binary64)
(*.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)

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

localize43.0ms (1%)

Memory

2.3MiB live, 40.3MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 #s(literal 1/2 binary64) x)
accuracy	0.0625	(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
accuracy	0.30078125	(*.f64 #s(literal 1/24 binary64) x)
accuracy	31.471016495589602	#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
accuracy	0	(/.f64 #s(literal 2 binary64) x)
accuracy	0.20703125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
accuracy	31.295315347723506	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))

Samples

34.0ms

256×

valid

Compiler

Compiled 102 to 32 computations (68.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-tan: 9.0ms (36% of total)

ival-mult: 6.0ms (24% of total)

ival-div: 5.0ms (20% of total)

const: 4.0ms (16% of total)

ival-add: 1.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

8 → 96

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/24 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 #s(literal 1/2 binary64) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

-inf

((/ 1 (/ 2 x)) (tan (/ x 2)) (/ 2 x) (+ (* (* x x) (* 1/24 x)) (* 1/2 x)) (tan (/ x 2)) (* x x) (* 1/24 x) (* 1/2 x))

2.0ms

inf

((/ 1 (/ 2 x)) (tan (/ x 2)) (/ 2 x) (+ (* (* x x) (* 1/24 x)) (* 1/2 x)) (tan (/ x 2)) (* x x) (* 1/24 x) (* 1/2 x))

1.0ms

((/ 1 (/ 2 x)) (tan (/ x 2)) (/ 2 x) (+ (* (* x x) (* 1/24 x)) (* 1/2 x)) (tan (/ x 2)) (* x x) (* 1/24 x) (* 1/2 x))

simplify234.0ms (5.4%)

Memory

2.3MiB live, 150.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	514
1	99	514
2	247	514
3	567	514
4	918	514
5	1630	514
6	2914	514
7	3972	514
8	4653	514
9	5250	514
10	6056	514
11	6408	514
12	6636	514
13	6830	514
14	7016	514
15	7207	514
0	8383	493

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

Inputs
(* 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))))))))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 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))))
(* 1/2 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))))))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 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)
(/ (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)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 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)))))
(/ (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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 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)
(/ (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)))
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(* 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)))))
(/ (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)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/24 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)

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

rewrite162.0ms (3.7%)

Memory

4.2MiB live, 128.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	52
0	22	48
1	72	46
2	469	46
3	5022	46
0	9822	44

Stop Event

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

Counts

8 → 341

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
(/.f64 #s(literal 2 binary64) x)
(fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
(*.f64 x x)
(*.f64 #s(literal 1/24 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval69.0ms (1.6%)

Memory: -0.2MiB live, 122.9MiB allocated
Compiler: Compiled 8 245 to 1 029 computations (87.5% saved)

prune15.0ms (0.3%)

Memory

1.0MiB live, 37.7MiB allocated

Pruning

8 alts after pruning (2 fresh and 6 done)

	Pruned	Kept	Total
New	435	2	437
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	435	8	443

Accuracy

100.0%

Counts

443 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	50.8%	#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
✓	50.9%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
▶	3.7%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
✓	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
▶	3.7%	#s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64)))
✓	51.1%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 86 to 69 computations (19.8% saved)

simplify3.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal -2 binary64) x)
cost-diff	0	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
cost-diff	0	(*.f64 x #s(literal -1/2 binary64))
cost-diff	0	#s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
0	15	30
1	19	30
0	19	30

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize53.0ms (1.2%)

Memory

-48.7MiB live, 55.9MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 #s(literal -2 binary64) x)
accuracy	0.20703125	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))
accuracy	61.65532964880974	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
accuracy	0	(*.f64 x #s(literal -1/2 binary64))
accuracy	61.65532964880974	#s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64)))

Samples

23.0ms

256×

valid

Compiler

Compiled 60 to 24 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-tan: 8.0ms (50.1% of total)

ival-div: 5.0ms (31.3% of total)

ival-mult: 2.0ms (12.5% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())
#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())

Outputs
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor 0 x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch #s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x))) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())
#s(alt #<batchref> (taylor -inf x) (#s(alt #<batchref> (patch (/.f64 #s(literal -2 binary64) x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((tan (/ x 2)) (* x -1/2) (/ 1 (/ -2 x)) (tan (/ x 2)) (/ -2 x))
1.0ms	x	@	-inf	((tan (/ x 2)) (* x -1/2) (/ 1 (/ -2 x)) (tan (/ x 2)) (/ -2 x))
1.0ms	x	@	inf	((tan (/ x 2)) (* x -1/2) (/ 1 (/ -2 x)) (tan (/ x 2)) (/ -2 x))

simplify16.0ms (0.4%)

Memory

27.4MiB live, 27.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	348
1	78	348
2	195	348
3	445	348
4	643	348
5	701	348
6	704	348
0	704	336

Stop Event

1×	iter limit
1×	saturated

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 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(* -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))))))))
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -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)
(/ (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)))
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -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)
(/ (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)))
(/ -2 x)
(/ -2 x)
(/ -2 x)
(/ -2 x)

Outputs
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal 1/2 binary64) x)
(.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x)
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 17/40320 binary64) (.f64 x x) #s(literal 1/240 binary64)) (.f64 x x) #s(literal 1/24 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(*.f64 #s(literal -1/2 binary64) x)
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)
(/.f64 #s(literal -2 binary64) x)

rewrite66.0ms (1.5%)

Memory

8.8MiB live, 82.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	29
0	15	25
1	44	25
2	134	25
3	457	25
0	2331	25

Stop Event

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

Counts

5 → 349

Calls

Call 1

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

Outputs
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eval56.0ms (1.3%)

Memory: 3.3MiB live, 118.0MiB allocated
Compiler: Compiled 5 986 to 808 computations (86.5% saved)

prune22.0ms (0.5%)

Memory

-1.5MiB live, 76.2MiB allocated

Pruning

18 alts after pruning (10 fresh and 8 done)

	Pruned	Kept	Total
New	399	10	409
Fresh	0	0	0
Picked	0	2	2
Done	0	6	6
Total	399	18	417

Accuracy

100.0%

Counts

417 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
✓	50.8%	#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
	3.9%	#s(approx (tan (/ x 2)) (/.f64 (.f64 (neg.f64 (.f64 x x)) #s(literal 1/2 binary64)) x))
	3.7%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))))
	50.6%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x))) (neg.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x))))))
✓	50.9%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
	3.7%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))))))
✓	3.7%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
	4.0%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (neg.f64 (.f64 x x))) x)))
	27.2%	#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -2 binary64) (neg.f64 (.f64 x x))) x)))
✓	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
✓	50.8%	#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
	3.7%	#s(approx (tan (/ x 2)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x))))
	50.6%	#s(approx (tan (/ x 2)) (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x))))
	50.7%	#s(approx (tan (/ x 2)) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x))))
	3.7%	#s(approx (tan (/ x 2)) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)) (neg.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x)))))
✓	3.7%	#s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64)))
✓	51.1%	#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))

Compiler

Compiled 513 to 264 computations (48.5% saved)

regimes29.0ms (0.7%)

Memory

-29.4MiB live, 21.4MiB allocated

Counts

20 → 1

Calls

Call 1

Inputs
#s(approx (tan (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (tan (/ x 2)) (*.f64 x #s(literal -1/2 binary64)))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (fma.f64 (.f64 x x) (.f64 #s(literal 1/24 binary64) x) (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -2 binary64) x)))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)))
#s(approx (tan (/ x 2)) (/.f64 (.f64 (neg.f64 (.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (.f64 (fma.f64 (fma.f64 #s(literal 1/240 binary64) (.f64 x x) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal -2 binary64) (neg.f64 (.f64 x x))) x)))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 #s(literal 2 binary64) (neg.f64 (.f64 x x))) x)))
#s(approx (tan (/ x 2)) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (tan (/ x 2)) (.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)) (neg.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x)))))
#s(approx (tan (/ x 2)) (.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (tan (/ x 2)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) x))))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x))) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x))) (neg.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x))))))
#s(approx (tan (/ x 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (.f64 #s(literal 1/2 binary64) x)))))))
(tan.f64 (*.f64 x #s(literal 1/2 binary64)))
(tan.f64 (/.f64 x #s(literal 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:

22.0ms	x
6.0ms	(/.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 8 to 7 computations (12.5% saved)

regimes12.0ms (0.3%)

Memory

14.5MiB live, 14.5MiB allocated

Accuracy

Total -31.2b remaining (-99.7%)

Threshold costs -31.2b (-99.7%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

2 calls:

5.0ms	x
5.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Results

Accuracy	Segments	Branch
51.1%	1	`x`
51.1%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify39.0ms (0.9%)

Memory

-20.7MiB live, 19.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	10	12

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness176.0ms (4%)

Memory

5.0MiB live, 44.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
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
0	4	7
0	6	7
1	19	7
2	51	7
3	188	7
4	888	7
0	8099	7
0	26	156
1	73	156
2	190	156
3	441	156
4	653	156
5	711	156
6	714	156
0	714	150

Stop Event

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

Compiler

Compiled 45 to 36 computations (20% saved)

preprocess36.0ms (0.8%)

Memory: 11.6MiB live, 50.2MiB allocated
Remove: (negabs x)
Compiler: Compiled 62 to 52 computations (16.1% 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	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

start0.0ms (0%)

analyze110.0ms (2.5%)

sample2.0s (46.5%)

explain225.0ms (5.2%)

preprocess42.0ms (1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize22.0ms (0.5%)

series3.0ms (0.1%)

simplify15.0ms (0.3%)

rewrite113.0ms (2.6%)

eval110.0ms (2.5%)

prune19.0ms (0.4%)

simplify7.0ms (0.2%)

localize108.0ms (2.5%)

series9.0ms (0.2%)

simplify191.0ms (4.4%)

rewrite181.0ms (4.2%)

eval105.0ms (2.4%)

prune19.0ms (0.4%)

simplify4.0ms (0.1%)

localize43.0ms (1%)

series6.0ms (0.1%)

simplify234.0ms (5.4%)

rewrite162.0ms (3.7%)

eval69.0ms (1.6%)

prune15.0ms (0.3%)

simplify3.0ms (0.1%)

localize53.0ms (1.2%)

series3.0ms (0.1%)

simplify16.0ms (0.4%)

rewrite66.0ms (1.5%)

eval56.0ms (1.3%)

prune22.0ms (0.5%)

regimes29.0ms (0.7%)

regimes12.0ms (0.3%)

simplify39.0ms (0.9%)

soundness176.0ms (4%)

preprocess36.0ms (0.8%)

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