Metrics for Hyperbolic arc-(co)secant

start0.0ms (0%)

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

analyze3.0ms (0.2%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms 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%	50%	0%	0%	50%	0%	3
33.3%	12.5%	25%	0%	0%	62.5%	0%	4
60%	18.7%	12.5%	0%	0%	68.7%	0%	5
77.8%	21.9%	6.2%	0%	0%	71.8%	0%	6
88.2%	23.4%	3.1%	0%	0%	73.4%	0%	7
93.9%	24.2%	1.6%	0%	0%	74.2%	0%	8
96.9%	24.6%	0.8%	0%	0%	74.6%	0%	9
98.4%	24.8%	0.4%	0%	0%	74.8%	0%	10
99.2%	24.9%	0.2%	0%	0%	74.9%	0%	11
99.6%	24.9%	0.1%	0%	0%	74.9%	0%	12

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample964.0ms (81.3%)

Memory

32.1MiB live, 944.2MiB allocated; 332ms collecting garbage

Samples

740.0ms	8 255×	0	valid
2.0ms	25×	0	invalid
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 501.0ms

ival-div!: 145.0ms (29% of total)

ival-log: 126.0ms (25.2% of total)

ival-mult!: 122.0ms (24.4% of total)

ival-sqrt: 61.0ms (12.2% of total)

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

ival-sub!: 20.0ms (4% of total)

adjust: 1.0ms (0.2% of total)

Bogosity

preprocess33.0ms (2.8%)

Memory

2.3MiB live, 48.1MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	27
1	84	27
2	314	26
3	1097	26

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))

Compiler

Compiled 20 to 18 computations (10% saved)

series13.0ms (1.1%)

Memory

43.7MiB live, 43.7MiB allocated; 0ms collecting garbage

Counts

9 → 55

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 1 x) 1 x (/ (sqrt (- 1 (* x x))) x) (sqrt (- 1 (* x x))) (- 1 (* x x)) (* x x))
4.0ms	x	@	inf	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 1 x) 1 x (/ (sqrt (- 1 (* x x))) x) (sqrt (- 1 (* x x))) (- 1 (* x x)) (* x x))
2.0ms	x	@	0	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 1 x) 1 x (/ (sqrt (- 1 (* x x))) x) (sqrt (- 1 (* x x))) (- 1 (* x x)) (* x x))

Time

Variable

Point

Expression

5.0ms

-inf

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

4.0ms

inf

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

2.0ms

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

rewrite87.0ms (7.3%)

Memory

-18.1MiB live, 86.7MiB allocated; 62ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	256	1557
0	267	1543

Stop Event

1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

64 → 64

Calls

Call 1

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

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

eval12.0ms (1%)

Memory: -31.5MiB live, 16.3MiB allocated; 8ms collecting garbage
Compiler: Compiled 935 to 352 computations (62.4% saved)

prune2.0ms (0.1%)

Memory

3.1MiB live, 3.1MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	3	56

Accuracy

100.0%

Counts

56 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
▶	99.4%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
▶	0.0%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))

Status

Accuracy

Program

✓

100.0%

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

▶

99.4%

(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))

▶

0.0%

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

Compiler

Compiled 34 to 33 computations (2.9% saved)

series9.0ms (0.8%)

Memory

15.1MiB live, 15.1MiB allocated; 0ms collecting garbage

Counts

9 → 27

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) -1 (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) 2 x)
3.0ms	x	@	-inf	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) -1 (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) 2 x)
2.0ms	x	@	0	((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) -1 (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) 2 x)

Time

Variable

Point

Expression

3.0ms

inf

((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) -1 (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) 2 x)

3.0ms

-inf

((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) -1 (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) 2 x)

2.0ms

((log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt -1) -1 (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))) (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/ 2 x) 2 x)

rewrite25.0ms (2.1%)

Memory

-14.5MiB live, 30.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	185	904
0	187	891

Stop Event

1×	iter-limit
1×	iter-limit
1×	unsound
1×	iter-limit

Counts

36 → 36

Calls

Call 1

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

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

eval3.0ms (0.2%)

Memory: 3.8MiB live, 3.8MiB allocated; 0ms collecting garbage
Compiler: Compiled 468 to 192 computations (59% saved)

prune2.0ms (0.2%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	25	3	28

Accuracy

100.0%

Counts

28 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))
✓	99.4%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))
✓	0.0%	(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (sqrt.f64 #s(literal -1 binary64))))

Status

Accuracy

Program

✓

100.0%

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

✓

99.4%

(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))

✓

0.0%

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

Compiler

Compiled 65 to 57 computations (12.3% saved)

regimes5.0ms (0.4%)

Memory

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

Counts

3 → 1

Calls

Call 1

Inputs

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

(log.f64 #s(approx (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)) (/.f64 #s(literal 2 binary64) x)))

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

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

Calls

3 calls:

2.0ms

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

2.0ms

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

1.0ms

Results

Accuracy	Segments	Branch
100.0%	1	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`
100.0%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
100.0%	1	`x`

Compiler

Compiled 20 to 18 computations (10% saved)

regimes4.0ms (0.4%)

Memory

12.0MiB live, 12.0MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms

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

1.0ms

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

1.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`
99.4%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
99.4%	1	`x`

Compiler

Compiled 20 to 18 computations (10% saved)

regimes3.0ms (0.3%)

Memory

11.0MiB live, 11.0MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

1.0ms

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

1.0ms

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

1.0ms

Results

Accuracy	Segments	Branch
0.0%	1	`(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x))`
0.0%	1	`(log.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) x)))`
0.0%	1	`x`

Compiler

Compiled 20 to 18 computations (10% saved)

derivations2.0ms (0.2%)

Memory

1.5MiB live, 1.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 31 to 24 computations (22.6% saved)

preprocess20.0ms (1.7%)

Memory: -0.0MiB live, 46.3MiB allocated; 2ms collecting garbage
Compiler: Compiled 41 to 33 computations (19.5% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze3.0ms (0.2%)

sample964.0ms (81.3%)

preprocess33.0ms (2.8%)

series13.0ms (1.1%)

rewrite87.0ms (7.3%)

eval12.0ms (1%)

prune2.0ms (0.1%)

series9.0ms (0.8%)

rewrite25.0ms (2.1%)

eval3.0ms (0.2%)

prune2.0ms (0.2%)

regimes5.0ms (0.4%)

regimes4.0ms (0.4%)

regimes3.0ms (0.3%)

derivations2.0ms (0.2%)

preprocess20.0ms (1.7%)

end0.0ms (0%)

Profiling