Metrics for tanhf (example 3.4)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze170.0ms (5.8%)

Memory

-24.3MiB live, 125.3MiB allocated; 54ms collecting garbage

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)

sample2.1s (70.8%)

Memory

44.4MiB live, 2 352.0MiB allocated; 308ms collecting garbage

Samples

743.0ms	2 212×	2	valid
516.0ms	4 187×	0	valid
339.0ms	664×	3	valid
157.0ms	1 188×	1	valid
6.0ms	5×	4	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

ival-cos: 784.0ms (52.6% of total)

adjust: 260.0ms (17.4% of total)

ival-sin: 242.0ms (16.2% of total)

ival-div: 107.0ms (7.2% of total)

ival-sub: 87.0ms (5.8% of total)

exact: 7.0ms (0.5% of total)

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

Bogosity

explain137.0ms (4.7%)

Memory

-14.5MiB live, 181.6MiB allocated; 5ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
75	1	(-1040718764963011200.0)	3	(-3.106778720075188e+244)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
53	0	-	4	(4.115380366228996e-156)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(sin.f64 x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	73	7
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))`	u/n	49	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	49

Confusion

	Predicted +	Predicted -
+	121	3
-	1	131

Precision

0.9918032786885246

Recall

0.9758064516129032

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	121	3	0
-	1	4	127

Precision?

0.9612403100775194

Recall?

1.0

Freqs

test

number	freq
0	134
1	122

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms	102×	2	valid
31.0ms	292×	0	valid
18.0ms	36×	3	valid
10.0ms	82×	1	valid

Compiler

Compiled 45 to 22 computations (51.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 75.0ms

ival-cos: 42.0ms (56.3% of total)

ival-sin: 12.0ms (16.1% of total)

adjust: 9.0ms (12.1% of total)

ival-div: 6.0ms (8% of total)

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

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

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

exact: 0.0ms (0% of total)

preprocess142.0ms (4.8%)

Memory

15.4MiB live, 159.5MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	13
1	40	13
2	78	12
3	152	12
4	392	12
5	1447	12
0	6	7
0	10	4
1	24	4
2	37	4
3	60	4
4	131	4
5	606	4
0	8288	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	59.0%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

series3.0ms (0.1%)

Memory

3.4MiB live, 3.4MiB allocated; 0ms collecting garbage

Counts

6 → 21

Calls

Call 1

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

Outputs
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* 1/2 (pow x 2))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))))
#s(approx (- 1 (cos x)) #s(hole binary64 (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))))
#s(approx (cos x) #s(hole binary64 1))
#s(approx (cos x) #s(hole binary64 (+ 1 (* -1/2 (pow x 2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))))
#s(approx (cos x) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))))
#s(approx x #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 x))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* -1/6 (pow x 2))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))))
#s(approx (sin x) #s(hole binary64 (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))))
#s(approx (/ (- 1 (cos x)) (sin x)) #s(hole binary64 (/ (- 1 (cos x)) (sin x))))
#s(approx (- 1 (cos x)) #s(hole binary64 (- 1 (cos x))))
#s(approx (cos x) #s(hole binary64 (cos x)))
#s(approx (sin x) #s(hole binary64 (sin x)))

Calls

3 calls:

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

rewrite148.0ms (5.1%)

Memory

-7.0MiB live, 134.9MiB allocated; 6ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	104	320
0	110	299
1	582	299
0	4946	281

Stop Event

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

Counts

27 → 56

Calls

Call 1

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

Outputs
(/.f64 (-.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))) (fma.f64 #s(literal 1 binary64) (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (/.f64 (cos.f64 x) (sin.f64 x)) #s(literal 3 binary64))) (+.f64 (.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (pow.f64 (sin.f64 x) #s(literal -1 binary64))) (fma.f64 (/.f64 (cos.f64 x) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)) (.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)))) (neg.f64 (neg.f64 (sin.f64 x))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (sin.f64 x)) (.f64 (sin.f64 x) (cos.f64 x))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (*.f64 (fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (*.f64 (+.f64 (fma.f64 (cos.f64 x) #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)) (sin.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (sin.f64 x) (fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(neg.f64 (/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (sin.f64 x)))
(neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (neg.f64 (sin.f64 x))))
(tan.f64 (+.f64 (/.f64 x #s(literal 2 binary64)) (PI.f64)))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (pow.f64 (sin.f64 x) #s(literal -1 binary64)) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64)))) (neg.f64 (fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (fma.f64 (cos.f64 x) #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) (fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (+.f64 (fma.f64 (cos.f64 x) #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 2 binary64)) (fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (cos.f64 x) #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))) (/.f64 (pow.f64 (cos.f64 x) #s(literal 3 binary64)) (+.f64 (fma.f64 (cos.f64 x) #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 2 binary64))) #s(literal 1 binary64))))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
#s(literal 1 binary64)
(*.f64 (cos.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (cos.f64 x))
(/.f64 (*.f64 #s(literal 2 binary64) (cos.f64 x)) #s(literal 2 binary64))
(fma.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (neg.f64 x) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) x))
(cos.f64 (neg.f64 (neg.f64 x)))
(cos.f64 (neg.f64 x))
(cos.f64 x)
(+.f64 (.f64 (sin.f64 x) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 x) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
x
(sin.f64 x)
#s(approx (/ (- 1 (cos x)) (sin x)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin 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(approx (/ (- 1 (cos x)) (sin 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))
#s(approx (- 1 (cos x)) (.f64 (.f64 x x) #s(literal 1/2 binary64)))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 #s(literal -1/24 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (.f64 (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/720 binary64) (.f64 x x)) #s(literal 1/24 binary64)) (*.f64 x x) #s(literal 1/2 binary64)) x) x))
#s(approx (- 1 (cos x)) (fma.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/40320 binary64) (.f64 x x) #s(literal 1/720 binary64)) x) x) #s(literal 1/24 binary64)) (.f64 (.f64 x x) #s(literal 1/2 binary64))))
#s(approx (cos x) #s(literal 1 binary64))
#s(approx (cos x) (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/24 binary64)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos x) (fma.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/720 binary64) (*.f64 x x) #s(literal 1/24 binary64)) x) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
#s(approx x x)
#s(approx (sin x) x)
#s(approx (sin x) (.f64 (fma.f64 (.f64 #s(literal -1/6 binary64) (*.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64)) x))
#s(approx (sin x) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/120 binary64) (.f64 x x)) #s(literal 1/6 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sin x) (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/5040 binary64) (*.f64 x x) #s(literal 1/120 binary64)) x) x) #s(literal 1/6 binary64)) x))
#s(approx (/ (- 1 (cos x)) (sin x)) (/.f64 (sin.f64 x) (fma.f64 (cos.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))))
#s(approx (- 1 (cos x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
#s(approx (cos x) (cos.f64 x))
#s(approx (sin x) (sin.f64 x))

eval7.0ms (0.2%)

Memory: 12.4MiB live, 12.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 865 to 229 computations (73.5% saved)

prune7.0ms (0.2%)

Memory

8.5MiB live, 8.5MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	2	59

Accuracy

100.0%

Counts

59 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
▶	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

series4.0ms (0.1%)

Memory

5.1MiB live, 5.1MiB allocated; 0ms collecting garbage

Counts

7 → 22

Calls

Call 1

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

Outputs
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx (cos (/ x 2)) #s(hole binary64 1))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (sin (/ x 2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (/ x 2)) #s(hole binary64 (cos (* 1/2 x))))

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

((tan (/ x 2)) (/ x 2) x 2 (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))

1.0ms

-inf

((tan (/ x 2)) (/ x 2) x 2 (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))

1.0ms

((tan (/ x 2)) (/ x 2) x 2 (/ (sin (/ x 2)) (cos (/ x 2))) (sin (/ x 2)) (cos (/ x 2)))

rewrite106.0ms (3.6%)

Memory

-13.1MiB live, 81.2MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	94	371
0	101	331
1	486	331
0	3779	311

Stop Event

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

Counts

29 → 63

Calls

Call 1

Inputs
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(cos.f64 (/.f64 x #s(literal 2 binary64)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (tan (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (/ x 2) #s(hole binary64 (* 1/2 x)))
#s(approx x #s(hole binary64 x))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* 1/2 x)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* 1/24 (pow x 2))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* 1/2 x)))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* -1/48 (pow x 2))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* 1/3840 (pow x 2)) 1/48))))))
#s(approx (sin (/ x 2)) #s(hole binary64 (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/3840 (* -1/645120 (pow x 2)))) 1/48))))))
#s(approx (cos (/ x 2)) #s(hole binary64 1))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* -1/8 (pow x 2)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* 1/384 (pow x 2)) 1/8)))))
#s(approx (cos (/ x 2)) #s(hole binary64 (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/384 (* -1/46080 (pow x 2)))) 1/8)))))
#s(approx (tan (/ x 2)) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) #s(hole binary64 (/ (sin (* 1/2 x)) (cos (* 1/2 x)))))
#s(approx (sin (/ x 2)) #s(hole binary64 (sin (* 1/2 x))))
#s(approx (cos (/ x 2)) #s(hole binary64 (cos (* 1/2 x))))

Outputs
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal -2 binary64)))) (neg.f64 (cos.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64)))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (+.f64 (/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (tan.f64 (PI.f64)))))
(/.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) (cos.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64))))
(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64))))
(neg.f64 (/.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64)))))
(neg.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64)))))
(tan.f64 (+.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))
(/.f64 (neg.f64 (neg.f64 x)) #s(literal 2 binary64))
(/.f64 (neg.f64 x) #s(literal -2 binary64))
(/.f64 x #s(literal 2 binary64))
(neg.f64 (/.f64 x #s(literal -2 binary64)))
x
#s(literal 2 binary64)
(/.f64 (neg.f64 (sin.f64 (/.f64 x #s(literal -2 binary64)))) (neg.f64 (cos.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64)))))
(/.f64 (neg.f64 (sin.f64 x)) (neg.f64 (+.f64 (cos.f64 x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x))) (neg.f64 (sin.f64 x)))
(/.f64 (+.f64 (/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (tan.f64 (PI.f64))) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64))) (tan.f64 (PI.f64)))))
(/.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) (cos.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64))))
(/.f64 (sin.f64 x) (+.f64 (cos.f64 x) #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64))))
(neg.f64 (/.f64 (sin.f64 (/.f64 x #s(literal -2 binary64))) (cos.f64 (/.f64 x #s(literal -2 binary64)))))
(neg.f64 (/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (PI.f64)))))
(tan.f64 (+.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))) (PI.f64)))
(tan.f64 (+.f64 (PI.f64) (/.f64 x #s(literal 2 binary64))))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) (/.f64 (cos.f64 x) (sin.f64 x)))
(sin.f64 (/.f64 x #s(literal 2 binary64)))
(fma.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64))) (*.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
(sin.f64 (+.f64 (/.f64 x #s(literal -2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))))
(sin.f64 (/.f64 (+.f64 x (PI.f64)) #s(literal 2 binary64)))
(cos.f64 (/.f64 x #s(literal -2 binary64)))
(cos.f64 (/.f64 x #s(literal 2 binary64)))
(+.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))) (.f64 (cos.f64 (/.f64 x #s(literal -2 binary64))) (sin.f64 (/.f64 (PI.f64) #s(literal 2 binary64)))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (sin (/ x 2)) (cos (/ 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 (/ (sin (/ x 2)) (cos (/ x 2))) (.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))
#s(approx (/ x 2) (*.f64 #s(literal 1/2 binary64) x))
#s(approx x x)
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/24 binary64) #s(literal 1/2 binary64)) x))
#s(approx (/ (sin (/ x 2)) (cos (/ 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 (/ (sin (/ x 2)) (cos (/ x 2))) (.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))
#s(approx (sin (/ x 2)) (*.f64 #s(literal 1/2 binary64) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 #s(literal -1/48 binary64) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (.f64 (fma.f64 (-.f64 (.f64 #s(literal 1/3840 binary64) (.f64 x x)) #s(literal 1/48 binary64)) (.f64 x x) #s(literal 1/2 binary64)) x))
#s(approx (sin (/ x 2)) (fma.f64 (.f64 x (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/645120 binary64) (.f64 x x) #s(literal 1/3840 binary64)) x) x) #s(literal 1/48 binary64)) (.f64 #s(literal 1/2 binary64) x)))
#s(approx (cos (/ x 2)) #s(literal 1 binary64))
#s(approx (cos (/ x 2)) (fma.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1 binary64) #s(literal 1 binary64)))
#s(approx (cos (/ x 2)) (fma.f64 (-.f64 (.f64 #s(literal 1/384 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)))
#s(approx (cos (/ x 2)) (fma.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (.f64 (.f64 (fma.f64 #s(literal -1/46080 binary64) (*.f64 x x) #s(literal 1/384 binary64)) x) x) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) (tan.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))))
#s(approx (/ (sin (/ x 2)) (cos (/ x 2))) (tan.f64 (fma.f64 #s(literal 1/2 binary64) x (PI.f64))))
#s(approx (sin (/ x 2)) (sin.f64 (*.f64 #s(literal 1/2 binary64) x)))
#s(approx (cos (/ x 2)) (sin.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (PI.f64) #s(literal 2 binary64)))))

eval7.0ms (0.2%)

Memory: 12.6MiB live, 12.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 736 to 178 computations (75.8% saved)

prune58.0ms (2%)

Memory

-42.0MiB live, 26.3MiB allocated; 53ms collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	60	2	62

Accuracy

100.0%

Counts

62 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(/.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
✓	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))

Compiler

Compiled 33 to 22 computations (33.3% saved)

regimes3.0ms (0.1%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Accuracy

Total -26.3b remaining (-673487.9%)

Threshold costs -26.3b (-673487.9%)

Counts

3 → 1

Calls

Call 1

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify37.0ms (1.3%)

Memory

-17.3MiB live, 32.4MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	4
1	6	4
2	9	4
3	15	4
4	47	4
5	368	4
6	3459	4

Stop Event

1×	node limit

Calls

Call 1

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

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

derivations14.0ms (0.5%)

Memory

14.9MiB live, 14.9MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 4 to 4 computations (0% saved)

preprocess13.0ms (0.4%)

Memory: 21.2MiB live, 21.2MiB allocated; 0ms collecting garbage
Remove: (negabs x)
Compiler: Compiled 30 to 28 computations (6.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze170.0ms (5.8%)

sample2.1s (70.8%)

explain137.0ms (4.7%)

preprocess142.0ms (4.8%)

eval0.0ms (0%)

prune0.0ms (0%)

series3.0ms (0.1%)

rewrite148.0ms (5.1%)

eval7.0ms (0.2%)

prune7.0ms (0.2%)

series4.0ms (0.1%)

rewrite106.0ms (3.6%)

eval7.0ms (0.2%)

prune58.0ms (2%)

regimes3.0ms (0.1%)

simplify37.0ms (1.3%)

derivations14.0ms (0.5%)

preprocess13.0ms (0.4%)

end0.0ms (0%)

Profiling