Metrics for Hyperbolic arc-cosine

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze194.0ms (4.9%)

Memory

35.6MiB live, 115.5MiB allocated; 318ms 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
0%	0%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 9 computations (18.2% saved)

sample2.2s (57%)

Memory

68.2MiB live, 2 934.2MiB allocated; 877ms collecting garbage

Samples

1.2s	8 233×	1	invalid
550.0ms	8 256×	0	valid
15.0ms	317×	0	invalid

Precisions

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

ival-sqrt: 306.0ms (23.8% of total)

ival-log: 280.0ms (21.8% of total)

adjust: 271.0ms (21.1% of total)

ival-mult!: 200.0ms (15.6% of total)

ival-add!: 162.0ms (12.6% of total)

ival-sub!: 66.0ms (5.1% of total)

Bogosity

preprocess75.0ms (1.9%)

Memory

-25.4MiB live, 52.8MiB allocated; 57ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	9
1	47	9
2	89	9
3	200	9
4	969	9

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	55.7%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 14 to 14 computations (0% saved)

series6.0ms (0.2%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Counts

7 → 39

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
x
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)

Outputs
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (log (sqrt -1))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (sqrt -1)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (- (* x x) 1) #s(hole binary64 -1))
#s(approx (- (* x x) 1) #s(hole binary64 (- (pow x 2) 1)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (* x x) 1) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 1/2) (log (/ 1 x)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/4 (* 5/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 5/32 (* 11/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ 1/2 x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) x (sqrt (- (* x x) 1)) (- (* x x) 1) (* x x) 1)
2.0ms	x	@	inf	((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) x (sqrt (- (* x x) 1)) (- (* x x) 1) (* x x) 1)
2.0ms	x	@	-inf	((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) x (sqrt (- (* x x) 1)) (- (* x x) 1) (* x x) 1)

Time

Variable

Point

Expression

2.0ms

((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) x (sqrt (- (* x x) 1)) (- (* x x) 1) (* x x) 1)

2.0ms

inf

((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) x (sqrt (- (* x x) 1)) (- (* x x) 1) (* x x) 1)

2.0ms

-inf

((log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) x (sqrt (- (* x x) 1)) (- (* x x) 1) (* x x) 1)

rewrite81.0ms (2.1%)

Memory

27.7MiB live, 75.0MiB allocated; 36ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	198	966
0	205	706
0	1187	676

Stop Event

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

Counts

46 → 61

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
x
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1 binary64)
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (log (sqrt -1))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (sqrt -1)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (+ (sqrt -1) (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (+ (sqrt -1) (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (- (* x x) 1) #s(hole binary64 -1))
#s(approx (- (* x x) 1) #s(hole binary64 (- (pow x 2) 1)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* 2 x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (- (* x x) 1) #s(hole binary64 (* (pow x 2) (- 1 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 1/2) (log (/ 1 x)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/4 (* 5/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 5/32 (* 11/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ 1/2 x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 x)))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 (* x (- 1 (* 1/2 (/ 1 (pow x 2))))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2))))))))
#s(approx (sqrt (- (* x x) 1)) #s(hole binary64 (* -1 (* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2))))))))

Outputs
(acosh.f64 x)
(log.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))))) (-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) #s(literal 1 binary64)))))))
(+.f64 (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) x)
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
x
(pow.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sinh.f64 (acosh.f64 x))
(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1 binary64)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 (.f64 x x) (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))))
(expm1.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(-.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 1 binary64)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
#s(literal 1 binary64)
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (fma.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (+ x (sqrt (- (* x x) 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ x (sqrt (- (* x x) 1))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx x x)
#s(approx (sqrt (- (* x x) 1)) (fma.f64 (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- (* x x) 1)) (fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- (* x x) 1)) (fma.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (.f64 x x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x x) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (- (* x x) 1) #s(literal -1 binary64))
#s(approx (- (* x x) 1) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
#s(approx (* x x) (*.f64 x x))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 #s(literal 2 binary64)) (-.f64 (neg.f64 (neg.f64 (log.f64 x))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x x)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (-.f64 (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 2 binary64)) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x))
#s(approx (sqrt (- (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x))
#s(approx (sqrt (- (* x x) 1)) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64)) x))
#s(approx (sqrt (- (* x x) 1)) (.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x))
#s(approx (- (* x x) 1) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (*.f64 x x)))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (log.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (-.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (-.f64 (+.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 11/96 binary64) (.f64 x x)) #s(literal 5/32 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
#s(approx (+ x (sqrt (- (* x x) 1))) (/.f64 #s(literal 1/2 binary64) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x))) #s(literal 1/2 binary64)) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (neg.f64 (/.f64 (-.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))
#s(approx (sqrt (- (* x x) 1)) (neg.f64 x))
#s(approx (sqrt (- (* x x) 1)) (.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))))
#s(approx (sqrt (- (* x x) 1)) (.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64))))
#s(approx (sqrt (- (* x x) 1)) (.f64 (neg.f64 x) (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))))

eval20.0ms (0.5%)

Memory: -32.1MiB live, 11.6MiB allocated; 16ms collecting garbage
Compiler: Compiled 666 to 306 computations (54.1% saved)

prune1.0ms (0%)

Memory

2.9MiB live, 2.9MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	2	56

Accuracy

100.0%

Counts

56 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
▶	99.6%	(acosh.f64 x)

Compiler

Compiled 11 to 11 computations (0% saved)

series3.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

5 → 25

Calls

Call 1

Inputs
(acosh.f64 x)
x
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 x x)

Outputs
#s(approx (acosh x) #s(hole binary64 (log (sqrt -1))))
#s(approx (acosh x) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (acosh x) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (acosh x) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))))
#s(approx x #s(hole binary64 x))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (sqrt -1)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (acosh x) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (acosh x) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (acosh x) #s(hole binary64 (+ (log 1/2) (log (/ 1 x)))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (acosh x) #s(hole binary64 (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/4 (* 5/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 5/32 (* 11/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ 1/2 x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))
1.0ms	x	@	inf	((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))
1.0ms	x	@	0	((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

Time

Variable

Point

Expression

1.0ms

-inf

((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

1.0ms

inf

((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

1.0ms

((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (+ x x))

rewrite111.0ms (2.8%)

Memory

33.0MiB live, 71.6MiB allocated; 20ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	158	568
0	160	467
0	991	446

Stop Event

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

Counts

30 → 35

Calls

Call 1

Inputs
(acosh.f64 x)
x
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(+.f64 x x)
#s(approx (acosh x) #s(hole binary64 (log (sqrt -1))))
#s(approx (acosh x) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (acosh x) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (acosh x) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* (pow x 2) (- (* 3/40 (/ (pow x 2) (pow (sqrt -1) 5))) (* 1/6 (/ 1 (pow (sqrt -1) 3))))) (/ 1 (sqrt -1)))))))
#s(approx x #s(hole binary64 x))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (sqrt -1)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (acosh x) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (acosh x) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 3/32 (* 5/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* x (- (+ 2 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 4)))) (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (acosh x) #s(hole binary64 (+ (log 1/2) (log (/ 1 x)))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 1/2) (log (/ 1 x))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (acosh x) #s(hole binary64 (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 1/4 (* 5/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (acosh x) #s(hole binary64 (- (+ (log 1/2) (+ (log (/ 1 x)) (* -1 (/ (+ 5/32 (* 11/96 (/ 1 (pow x 2)))) (pow x 4))))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ 1/2 x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 (pow x 2)))) (pow x 2))) 1/2) x))))
#s(approx (+ x (sqrt (- (* x x) 1))) #s(hole binary64 (* -1 (/ (- (* -1 (/ (+ 1/16 (* 5/128 (/ 1 (pow x 2)))) (pow x 4))) (+ 1/2 (* 1/8 (/ 1 (pow x 2))))) x))))

Outputs
(acosh.f64 x)
(log.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) x))
x
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x))
(*.f64 #s(literal 2 binary64) x)
(*.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 x x) (.f64 x x)) (-.f64 x x))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 x x) (.f64 x x))))
(+.f64 x x)
#s(approx (acosh x) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
#s(approx (acosh x) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (acosh x) (fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (acosh x) (fma.f64 (fma.f64 (-.f64 (/.f64 (.f64 #s(literal 3/40 binary64) (.f64 x x)) (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) (/.f64 #s(literal 1/6 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))) (*.f64 x x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx x x)
#s(approx (+ x (sqrt (- (* x x) 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ x (sqrt (- (* x x) 1))) (fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 x x) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x #s(literal 1 binary64)) x (sqrt.f64 #s(literal -1 binary64))))
#s(approx (+ x x) (+.f64 x x))
#s(approx (acosh x) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))))
#s(approx (acosh x) (+.f64 (log.f64 #s(literal 2 binary64)) (-.f64 (neg.f64 (neg.f64 (log.f64 x))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x)))))
#s(approx (acosh x) (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 3/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (.f64 x x)))))
#s(approx (acosh x) (-.f64 (+.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/96 binary64) (.f64 x x)) #s(literal 3/32 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (*.f64 x x))))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 2 binary64)) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) x))
#s(approx (acosh x) (log.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))))
#s(approx (acosh x) (-.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
#s(approx (acosh x) (+.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/32 binary64) (.f64 x x)) #s(literal 1/4 binary64)) (*.f64 x x)))))
#s(approx (acosh x) (-.f64 (+.f64 (log.f64 (.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 11/96 binary64) (.f64 x x)) #s(literal 5/32 binary64)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 #s(literal 1/4 binary64) (.f64 x x))))
#s(approx (+ x (sqrt (- (* x x) 1))) (/.f64 #s(literal 1/2 binary64) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) (.f64 x x))) #s(literal 1/2 binary64)) x)))
#s(approx (+ x (sqrt (- (* x x) 1))) (neg.f64 (/.f64 (-.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x x)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x)))) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 x x))) x)))

eval7.0ms (0.2%)

Memory: 10.8MiB live, 10.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 342 to 181 computations (47.1% saved)

prune1.2s (29.8%)

Memory

-274.6MiB live, 51.1MiB allocated; 1.8s collecting garbage

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	31	2	33

Accuracy

100.0%

Counts

33 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
✓	99.6%	(acosh.f64 x)

Compiler

Compiled 27 to 27 computations (0% saved)

regimes5.0ms (0.1%)

Memory

11.8MiB live, 11.7MiB allocated; 0ms collecting garbage

Accuracy

Total -28.5b remaining (-12594.3%)

Threshold costs -28.5b (-12594.3%)

Counts

3 → 1

Calls

Call 1

Inputs
(acosh.f64 x)
(log.f64 #s(approx (+ x (sqrt (- (* x x) 1))) (+.f64 x x)))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Outputs
(acosh.f64 x)

Calls

3 calls:

2.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))
2.0ms	x
1.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.6%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`
99.6%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.6%	1	`x`

Compiler

Compiled 14 to 14 computations (0% saved)

derivations4.0ms (0.1%)

Memory

6.2MiB live, 6.2MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 2 to 2 computations (0% saved)

preprocess9.0ms (0.2%)

Memory: 18.6MiB live, 18.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 9 to 9 computations (0% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze194.0ms (4.9%)

sample2.2s (57%)

preprocess75.0ms (1.9%)

series6.0ms (0.2%)

rewrite81.0ms (2.1%)

eval20.0ms (0.5%)

prune1.0ms (0%)

series3.0ms (0.1%)

rewrite111.0ms (2.8%)

eval7.0ms (0.2%)

prune1.2s (29.8%)

regimes5.0ms (0.1%)

derivations4.0ms (0.1%)

preprocess9.0ms (0.2%)

end0.0ms (0%)

Profiling