Metrics for Hyperbolic arc-cosine

start0.0ms (0%)

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

analyze94.0ms (2.3%)

Memory

18.9MiB live, 115.6MiB allocated; 38ms 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)

sample2.6s (61.4%)

Memory

100.2MiB live, 3 567.8MiB allocated; 604ms collecting garbage

Samples

1.2s	7 894×	1	invalid
708.0ms	8 256×	0	valid
23.0ms	304×	0	invalid

Precisions

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

ival-log: 331.0ms (24.9% of total)

adjust: 269.0ms (20.3% of total)

ival-mult: 240.0ms (18.1% of total)

ival-sqrt: 212.0ms (16% of total)

ival-sub: 135.0ms (10.2% of total)

ival-add: 126.0ms (9.5% of total)

exact: 10.0ms (0.8% of total)

ival-assert: 5.0ms (0.4% of total)

Bogosity

explain101.0ms (2.4%)

Memory

-16.1MiB live, 174.2MiB allocated; 20ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
128	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
0	-	-	`(*.f64 x x)`
0	-	-	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))`	oflow-rescue	128	0
↳	`(-.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	128
↳	`(*.f64 x x)`	overflow	128

Confusion

	Predicted +	Predicted -
+	128	0
-	0	128

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	0	0
-	0	0	128

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	128
1	128

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

38.0ms

512×

valid

Compiler

Compiled 79 to 25 computations (68.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-log: 5.0ms (24.9% of total)

ival-sqrt: 5.0ms (24.9% of total)

ival-mult: 4.0ms (19.9% of total)

ival-add: 2.0ms (9.9% of total)

ival-sub: 2.0ms (9.9% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

preprocess213.0ms (5.1%)

Memory

-19.9MiB live, 130.4MiB allocated; 40ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	36	30
2	69	30
3	134	30
4	441	30
5	2697	30
6	6901	30
0	7	9
0	12	9
1	22	9
2	49	9
3	121	9
4	383	9
5	2335	9
6	7889	9
0	8019	6

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	51.6%	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

series6.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Counts

7 → 42

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

Time

Variable

Point

Expression

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

((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)

rewrite66.0ms (1.6%)

Memory

28.9MiB live, 75.0MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	202	988
0	210	724
0	1179	719

Stop Event

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

Counts

49 → 64

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)))
#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))
#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)))
#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)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))))
#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-product.f64 x #s(literal 1 binary64)) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (sqrt-product.f64 x #s(literal 1 binary64)) (sqrt-product.f64 x #s(literal 1 binary64)))) (-.f64 x (sqrt-product.f64 x #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (sqrt-product.f64 x #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (.f64 x x) (-.f64 (.f64 (sqrt-product.f64 x #s(literal 1 binary64)) (sqrt-product.f64 x #s(literal 1 binary64))) (*.f64 x (sqrt-product.f64 x #s(literal 1 binary64))))))
(+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x)
(+.f64 x (sqrt-product.f64 x #s(literal 1 binary64)))
x
(pow.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt-product.f64 x #s(literal 1 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 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 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 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.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)))) (+.f64 (.f64 (+.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64))) #s(literal -1/6 binary64))) x) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5/2 binary64))) #s(literal 3/40 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #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))) (+.f64 (.f64 (+.f64 (.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))) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64))))) x) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 binary64))))
#s(approx x x)
#s(approx (sqrt (- (* x x) 1)) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (sqrt (- (* x x) 1)) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- (* x x) 1)) (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1/8 binary64) (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64))))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- (* x x) 1)) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 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 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))))
#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) (pow.f64 x #s(literal -2 binary64))) #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) (pow.f64 x #s(literal -2 binary64))) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64))))) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))))
#s(approx (+ x (sqrt (- (* x x) 1))) (*.f64 #s(literal 2 binary64) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) #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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (sqrt (- (* x x) 1)) x)
#s(approx (sqrt (- (* x x) 1)) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (sqrt (- (* x x) 1)) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) #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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (- (* x x) 1) (*.f64 x x))
#s(approx (- (* x x) 1) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -2 binary64))) (.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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))) (-.f64 (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1/4 binary64) (pow.f64 x #s(literal -2 binary64))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) (+.f64 (log.f64 (.f64 #s(literal -1/2 binary64) (/.f64 #s(literal -1 binary64) x))) (+.f64 (-.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64)) (*.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal -6 binary64)))) (/.f64 #s(literal 3/32 binary64) (pow.f64 x #s(literal 4 binary64))))))
#s(approx (+ x (sqrt (- (* x x) 1))) (/.f64 #s(literal 1/2 binary64) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (/.f64 (+.f64 (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) x))
#s(approx (+ x (sqrt (- (* x x) 1))) (neg.f64 (/.f64 (-.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/16 binary64)) #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 5/128 binary64) (pow.f64 x #s(literal -2 binary64))) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))) 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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)))))
#s(approx (sqrt (- (* x x) 1)) (.f64 (neg.f64 x) (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) #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 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)))))

eval72.0ms (1.7%)

Memory

-20.4MiB live, 115.6MiB allocated; 20ms collecting garbage

Samples

26.0ms	512×	0	invalid
12.0ms	256×	0	valid

Compiler

Compiled 1 210 to 337 computations (72.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 10.0ms (59.1% of total)

ival-add: 2.0ms (11.8% of total)

ival-sqrt: 2.0ms (11.8% of total)

ival-sub: 1.0ms (5.9% of total)

ival-div: 1.0ms (5.9% of total)

ival-true: 1.0ms (5.9% of total)

adjust: 0.0ms (0% of total)

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

prune16.0ms (0.4%)

Memory

33.7MiB live, 33.7MiB allocated; 0ms collecting garbage

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	65	3	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	3	69

Accuracy

100.0%

Counts

69 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log.f64 (+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))
▶	98.9%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) x)))
▶	99.7%	(acosh.f64 x)

Samples

11.0ms

256×

valid

Compiler

Compiled 19 to 15 computations (21.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sqrt: 2.0ms (34% of total)

ival-sub: 1.0ms (17% of total)

ival-add: 1.0ms (17% of total)

ival-mult: 1.0ms (17% of total)

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

adjust: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

-33.5MiB live, 12.2MiB allocated; 4ms collecting garbage

Counts

9 → 85

Calls

Call 1

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

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 (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 (sqrt (- (* x x) 1)) #s(hole binary64 (sqrt -1)))
#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 (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (log (sqrt -1))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) 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 (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (sqrt -1)))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))))
#s(approx (sqrt (* (+ x 1) (- 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 1) (- 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 (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 (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))
#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 (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) 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 (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #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 1) (- x 1))) #s(hole binary64 x))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (sqrt (* (+ x 1) (- 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 (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)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))))
#s(approx (acosh x) #s(hole binary64 (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))))
#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)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))))
#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))))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (pow (sqrt -1) 2) 1)))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))))

Calls

3 calls:

Time	Variable		Point	Expression
6.0ms	x	@	-inf	((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (log (+ (sqrt (* (+ x 1) (- x 1))) x)) (+ (sqrt (* (+ x 1) (- x 1))) x) (sqrt (* (+ x 1) (- x 1))) 1)
1.0ms	x	@	inf	((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (log (+ (sqrt (* (+ x 1) (- x 1))) x)) (+ (sqrt (* (+ x 1) (- x 1))) x) (sqrt (* (+ x 1) (- x 1))) 1)
1.0ms	x	@	0	((acosh x) x (log (+ x (sqrt (- (* x x) 1)))) (+ x (sqrt (- (* x x) 1))) (sqrt (- (* x x) 1)) (log (+ (sqrt (* (+ x 1) (- x 1))) x)) (+ (sqrt (* (+ x 1) (- x 1))) x) (sqrt (* (+ x 1) (- x 1))) 1)

Time

Variable

Point

Expression

6.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

rewrite97.0ms (2.3%)

Memory

-6.4MiB live, 95.1MiB allocated; 10ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	327	2214
0	333	1589
0	1959	1577

Stop Event

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

Counts

94 → 108

Calls

Call 1

Inputs
(acosh.f64 x)
x
(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) x)))
(+.f64 x #s(approx (sqrt (- (* x x) 1)) x))
#s(approx (sqrt (- (* x x) 1)) x)
(log.f64 (+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))
(+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x)
(sqrt-product.f64 x #s(literal 1 binary64))
#s(literal 1 binary64)
#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 (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 (sqrt (- (* x x) 1)) #s(hole binary64 (sqrt -1)))
#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 (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (log (sqrt -1))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) 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 (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (sqrt -1)))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))))
#s(approx (sqrt (* (+ x 1) (- 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 1) (- 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 (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 (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))
#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 (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) 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 (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #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 1) (- x 1))) #s(hole binary64 x))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (sqrt (* (+ x 1) (- 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 (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)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))))
#s(approx (acosh x) #s(hole binary64 (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))))
#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)) (+ (/ 3/32 (pow x 4)) (* 1/4 (/ 1 (pow x 2))))))))
#s(approx (log (+ x (sqrt (- (* x x) 1)))) #s(hole binary64 (+ (log -1/2) (+ (log (/ -1 x)) (+ (/ 3/32 (pow x 4)) (+ (* 1/4 (/ 1 (pow x 2))) (* 5/96 (/ 1 (pow x 6)))))))))
#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))))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (sqrt (* (+ x 1) (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (pow (sqrt -1) 2) 1)))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))))
#s(approx (+ (sqrt (* (+ x 1) (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (* (+ x 1) (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))))

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

eval53.0ms (1.3%)

Memory

-1.1MiB live, 90.1MiB allocated; 10ms collecting garbage

Samples

18.0ms	512×	0	invalid
11.0ms	256×	0	valid

Compiler

Compiled 1 549 to 362 computations (76.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 7.0ms (52.3% of total)

ival-sqrt: 2.0ms (15% of total)

ival-sub: 1.0ms (7.5% of total)

ival-div: 1.0ms (7.5% of total)

ival-add: 1.0ms (7.5% of total)

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

adjust: 0.0ms (0% of total)

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

prune16.0ms (0.4%)

Memory

33.3MiB live, 33.3MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	0	0
Picked	0	3	3
Done	0	0	0
Total	76	4	80

Accuracy

100.0%

Counts

80 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))
▶	100.0%	(log.f64 (+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) x))
✓	98.9%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) x)))
✓	99.7%	(acosh.f64 x)

Samples

10.0ms

256×

valid

Compiler

Compiled 31 to 24 computations (22.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sqrt: 2.0ms (34.9% of total)

ival-sub: 1.0ms (17.4% of total)

ival-add: 1.0ms (17.4% of total)

ival-mult: 1.0ms (17.4% of total)

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

adjust: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

12.8MiB live, 12.8MiB allocated; 0ms collecting garbage

Counts

9 → 70

Calls

Call 1

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

Outputs
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (log (sqrt -1))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) 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 (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (sqrt -1)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- 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 (+ 1 x)) (sqrt (- 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 (sqrt (+ 1 x)) #s(hole binary64 1))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ 1 x) #s(hole binary64 1))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (- x 1) #s(hole binary64 -1))
#s(approx (- x 1) #s(hole binary64 (- x 1)))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) 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 (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #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 (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 x))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- 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 (sqrt (+ 1 x)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ 1 x) #s(hole binary64 x))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (pow (sqrt -1) 2) 1)))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (* (sqrt (+ 1 x)) (sqrt (- x 1))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- x 1)) (- x 1))
2.0ms	x	@	inf	((log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (* (sqrt (+ 1 x)) (sqrt (- x 1))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- x 1)) (- x 1))
1.0ms	x	@	0	((log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (* (sqrt (+ 1 x)) (sqrt (- x 1))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- x 1)) (- x 1))

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

1.0ms

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

rewrite102.0ms (2.4%)

Memory

-33.6MiB live, 109.9MiB allocated; 16ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	378	1954
0	388	1513
0	2407	1289

Stop Event

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

Counts

79 → 92

Calls

Call 1

Inputs
(log.f64 (+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) x))
(+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) x)
(*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (log (sqrt -1))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (/ x (sqrt -1)))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (sqrt -1)) (* x (+ (* -1/6 (/ (pow x 2) (pow (sqrt -1) 3))) (/ 1 (sqrt -1)))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) 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 (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (sqrt -1)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (+ x (sqrt -1))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* 1/2 (/ x (sqrt -1))))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (+ (sqrt -1) (* x (+ 1 (* x (+ (* -1/8 (/ (pow x 2) (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (sqrt -1)))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ (pow x 2) (sqrt -1))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- 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 (+ 1 x)) (sqrt (- 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 (sqrt (+ 1 x)) #s(hole binary64 1))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* 1/2 x))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* -1/8 x))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))))
#s(approx (+ 1 x) #s(hole binary64 1))
#s(approx (+ 1 x) #s(hole binary64 (+ 1 x)))
#s(approx x #s(hole binary64 x))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt -1)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))))
#s(approx (- x 1) #s(hole binary64 -1))
#s(approx (- x 1) #s(hole binary64 (- x 1)))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log 2) (* -1 (log (/ 1 x))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (- (+ (log 2) (* -1 (log (/ 1 x)))) (* 1/4 (/ 1 (pow x 2))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log 2) (+ (* -1 (log (/ 1 x))) (* -1 (/ (+ 1/4 (* 3/32 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) 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 (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* 2 x)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* x (- 2 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* x (+ 2 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #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 (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 x))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* x (- 1 (* 1/2 (/ 1 (pow x 2)))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (pow x 2)))) (pow x 2)))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- 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 (sqrt (+ 1 x)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))))
#s(approx (+ 1 x) #s(hole binary64 x))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (sqrt x)))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* -1/16 (sqrt (/ 1 (pow x 7))))))))))
#s(approx (- x 1) #s(hole binary64 x))
#s(approx (- x 1) #s(hole binary64 (* x (- 1 (/ 1 x)))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (* -1 (log (/ -1 x))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (* 1/2 (/ 1 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1))))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) #s(hole binary64 (+ (log (- (pow (sqrt -1) 2) 1)) (+ (* -1 (log (/ -1 x))) (+ (* -1/24 (/ (+ (* 3 (/ 1 (* (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) (* 3 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))) (pow x 4))) (+ (* 1/720 (/ (+ (* 45 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (+ (* 45 (/ 1 (* (pow (sqrt -1) 4) (- (pow (sqrt -1) 2) 1)))) (* 30 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))) (pow x 6))) (/ 1/2 (* (pow x 2) (- (pow (sqrt -1) 2) 1)))))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (pow (sqrt -1) 2) 1)))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) 1)))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (+ 1 (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2)))))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (+ 1 (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2))))))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2)) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 2))))))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) #s(hole binary64 (* -1 (* x (- (+ (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 4)))) (+ (* 1/2 (/ 1 (pow x 2))) (pow (sqrt -1) 2))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* (sqrt x) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- x 1)) #s(hole binary64 (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (pow (sqrt -1) 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (pow (sqrt -1) 2))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))))
#s(approx (- x 1) #s(hole binary64 (* -1 (* x (- (/ 1 x) 1)))))

Outputs
(log.f64 (+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))
(/.f64 (-.f64 (.f64 (sqrt-product.f64 x #s(literal 1 binary64)) (sqrt-product.f64 x #s(literal 1 binary64))) (.f64 x x)) (-.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))
(/.f64 (+.f64 (pow.f64 (sqrt-product.f64 x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (.f64 (sqrt-product.f64 x #s(literal 1 binary64)) (sqrt-product.f64 x #s(literal 1 binary64))) (-.f64 (.f64 x x) (*.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))))
(+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x)
(+.f64 x (sqrt-product.f64 x #s(literal 1 binary64)))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(*.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt-product.f64 x #s(literal 1 binary64))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (.f64 #s(literal 1 binary64) x))))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1 binary64)))))
(-.f64 x #s(literal 1 binary64))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (log.f64 (sqrt.f64 #s(literal -1 binary64))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (.f64 (+.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)) (.f64 (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64))) #s(literal -1/6 binary64))) x) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5/2 binary64))) #s(literal 3/40 binary64)) (/.f64 #s(literal 1/6 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) x) (log.f64 (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (+.f64 (sqrt.f64 #s(literal -1 binary64)) x))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (+.f64 (.f64 (+.f64 (.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 (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (*.f64 #s(literal -1/8 binary64) (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64))))) x) #s(literal 1 binary64)) x) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (+.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (+.f64 (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 #s(literal -1/8 binary64) (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3/2 binary64))))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (.f64 #s(literal 1/16 binary64) (ratio-of-squares.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5/2 binary64)))) (/.f64 #s(literal 1/8 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 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 (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (+ 1 x)) (+.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (+.f64 (.f64 (+.f64 (.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (*.f64 #s(literal 1/16 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)))
#s(approx (+ 1 x) #s(literal 1 binary64))
#s(approx (+ 1 x) (+.f64 x #s(literal 1 binary64)))
#s(approx x x)
#s(approx (sqrt (- x 1)) (sqrt.f64 #s(literal -1 binary64)))
#s(approx (sqrt (- x 1)) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 #s(literal -1/2 binary64) (/.f64 x (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (sqrt (- x 1)) (+.f64 (.f64 (+.f64 (.f64 (/.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64))) #s(literal -1/8 binary64)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- x 1)) (+.f64 (.f64 (+.f64 (.f64 (-.f64 (*.f64 (/.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 5/2 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal 1/8 binary64) (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)))) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (- x 1) #s(literal -1 binary64))
#s(approx (- x 1) (-.f64 x #s(literal 1 binary64)))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (-.f64 (+.f64 (neg.f64 (neg.f64 (log.f64 x))) (log.f64 #s(literal 2 binary64))) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) 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) (pow.f64 x #s(literal -2 binary64))) #s(literal 1/4 binary64)) (.f64 x x)))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) 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) (pow.f64 x #s(literal -2 binary64))) #s(literal 3/32 binary64)) (pow.f64 x #s(literal 4 binary64))))) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/4 binary64))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (*.f64 #s(literal 2 binary64) x))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (.f64 (-.f64 #s(literal 2 binary64) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 2 binary64)) x))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (.f64 (-.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (*.f64 x x))) #s(literal 1 binary64)) x))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (.f64 (-.f64 (+.f64 (neg.f64 (/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/16 binary64)) #s(literal 1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)) (*.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64))) x))
#s(approx (sqrt (+ 1 x)) (sqrt.f64 x))
#s(approx (sqrt (+ 1 x)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (pown3/2s.f64 x))) x))
#s(approx (sqrt (+ 1 x)) (.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (*.f64 #s(literal -1/2 binary64) (pown3/2s.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ 1 x)) (.f64 (+.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64)) (.f64 #s(literal -1/2 binary64) (pown3/2s.f64 x))) (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (+ 1 x) x)
#s(approx (+ 1 x) (*.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x))
#s(approx (sqrt (- x 1)) (sqrt.f64 x))
#s(approx (sqrt (- x 1)) (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 (pown3/2s.f64 x) #s(literal 1/2 binary64))) x))
#s(approx (sqrt (- x 1)) (.f64 (+.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (pown3/2s.f64 x)) (*.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (- x 1)) (.f64 (+.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1/16 binary64))) (.f64 #s(literal -1/2 binary64) (pown3/2s.f64 x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (- x 1) x)
#s(approx (- x 1) (*.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64))) x))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -2 binary64))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (-.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) (*.f64 #s(literal -1/2 binary64) (/.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)))) (log.f64 #s(literal -2 binary64))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -2 binary64))) (+.f64 (*.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) #s(literal 1/2 binary64)) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64))))))
#s(approx (log (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x)) (+.f64 (+.f64 (neg.f64 (log.f64 (/.f64 #s(literal -1 binary64) x))) (log.f64 #s(literal -2 binary64))) (+.f64 (+.f64 (/.f64 #s(literal -5/96 binary64) (pow.f64 x #s(literal 6 binary64))) (*.f64 (/.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal -3/32 binary64) (pow.f64 x #s(literal 4 binary64))))))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (neg.f64 (*.f64 #s(literal -2 binary64) x)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (neg.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)) x)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (neg.f64 (.f64 (-.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) x)))
#s(approx (+ (* (sqrt (+ 1 x)) (sqrt (- x 1))) x) (neg.f64 (.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal -2 binary64)) (/.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))))) x)))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (neg.f64 (*.f64 #s(literal -1 binary64) x)))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (neg.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) x)))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (neg.f64 (.f64 (-.f64 (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/8 binary64) (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) x)))
#s(approx (* (sqrt (+ 1 x)) (sqrt (- x 1))) (neg.f64 (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (+.f64 (.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)))) x)))
#s(approx (sqrt (+ 1 x)) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (sqrt (+ 1 x)) (neg.f64 (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (*.f64 (pown3/2s.f64 x) #s(literal 1/2 binary64))) x)))
#s(approx (sqrt (+ 1 x)) (neg.f64 (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (.f64 (pown3/2s.f64 x) #s(literal 1/2 binary64))) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))) x)))
#s(approx (sqrt (+ 1 x)) (neg.f64 (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal 1 binary64)) #s(literal 1/16 binary64))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)) (*.f64 (pown3/2s.f64 x) #s(literal 1/2 binary64)))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (*.f64 (sqrt.f64 x) #s(literal -1 binary64))))
#s(approx (sqrt (- x 1)) (neg.f64 (.f64 (+.f64 (.f64 (.f64 (pown3/2s.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64)) (+.f64 (.f64 (.f64 (pown3/2s.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)))) x)))
#s(approx (sqrt (- x 1)) (neg.f64 (.f64 (+.f64 (+.f64 (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -7 binary64))) #s(literal -1 binary64)) #s(literal 1/16 binary64)) (+.f64 (.f64 (.f64 (pown3/2s.f64 x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1 binary64)))) (.f64 (.f64 (sqrt.f64 (pow.f64 x #s(literal -5 binary64))) #s(literal -1 binary64)) #s(literal -1/8 binary64))) x)))
#s(approx (- x 1) (neg.f64 (*.f64 (-.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)) x)))

eval82.0ms (2%)

Memory

30.2MiB live, 129.1MiB allocated; 24ms collecting garbage

Samples

30.0ms	512×	0	invalid
23.0ms	512×	0	valid

Compiler

Compiled 2 170 to 566 computations (73.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 18.0ms (57.3% of total)

ival-sqrt: 3.0ms (9.5% of total)

ival-pow: 3.0ms (9.5% of total)

ival-div: 2.0ms (6.4% of total)

ival-add: 1.0ms (3.2% of total)

ival-sub: 1.0ms (3.2% of total)

ival-true: 1.0ms (3.2% of total)

adjust: 0.0ms (0% of total)

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

exact: 0.0ms (0% of total)

prune35.0ms (0.8%)

Memory

1.2MiB live, 47.4MiB allocated; 6ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	97	4	101

Accuracy

100.0%

Counts

101 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log.f64 (+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))
✓	100.0%	(log.f64 (+.f64 (*.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64)))) x))
✓	98.9%	(log.f64 (+.f64 x #s(approx (sqrt (- (* x x) 1)) x)))
✓	99.7%	(acosh.f64 x)

Samples

21.0ms

512×

valid

Compiler

Compiled 71 to 49 computations (31% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-add: 3.0ms (26.3% of total)

ival-mult: 3.0ms (26.3% of total)

ival-sqrt: 3.0ms (26.3% of total)

ival-sub: 2.0ms (17.5% of total)

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

adjust: 0.0ms (0% of total)

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

regimes11.0ms (0.3%)

Memory

-36.2MiB live, 10.5MiB allocated; 3ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

3 calls:

7.0ms	x
2.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))
2.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))

Results

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

Compiler

Compiled 18 to 14 computations (22.2% saved)

regimes4.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated; 0ms collecting garbage

Accuracy

Total -0.7b remaining (-450.2%)

Threshold costs -0.7b (-450.2%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(acosh.f64 x)

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.7%	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))))`
99.7%	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))))`
99.7%	1	`x`

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify49.0ms (1.2%)

Memory

1.9MiB live, 48.0MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	11	8
3	19	8
4	42	8
5	215	8
6	2137	8
7	5332	8

Stop Event

1×	node limit

Calls

Call 1

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

Outputs
(log.f64 (+.f64 (sqrt-product.f64 x #s(literal 1 binary64)) x))
(acosh.f64 x)

derivations19.0ms (0.4%)

Memory

32.5MiB live, 32.5MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Samples

10.0ms

256×

valid

Compiler

Compiled 8 to 6 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sqrt: 2.0ms (34.6% of total)

ival-sub: 1.0ms (17.3% of total)

ival-add: 1.0ms (17.3% of total)

ival-mult: 1.0ms (17.3% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess568.0ms (13.5%)

Memory

-10.1MiB live, 899.7MiB allocated; 127ms collecting garbage

Samples

418.0ms

8 256×

valid

Compiler

Compiled 34 to 26 computations (23.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 245.0ms

ival-mult: 88.0ms (36% of total)

ival-sqrt: 55.0ms (22.5% of total)

ival-add: 47.0ms (19.2% of total)

ival-sub: 45.0ms (18.4% of total)

ival-true: 5.0ms (2% of total)

ival-assert: 3.0ms (1.2% of total)

adjust: 2.0ms (0.8% of total)

end0.0ms (0%)

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

start0.0ms (0%)

analyze94.0ms (2.3%)

sample2.6s (61.4%)

explain101.0ms (2.4%)

preprocess213.0ms (5.1%)

eval0.0ms (0%)

prune0.0ms (0%)

series6.0ms (0.1%)

rewrite66.0ms (1.6%)

eval72.0ms (1.7%)

prune16.0ms (0.4%)

series9.0ms (0.2%)

rewrite97.0ms (2.3%)

eval53.0ms (1.3%)

prune16.0ms (0.4%)

series6.0ms (0.1%)

rewrite102.0ms (2.4%)

eval82.0ms (2%)

prune35.0ms (0.8%)

regimes11.0ms (0.3%)

regimes4.0ms (0.1%)

simplify49.0ms (1.2%)

derivations19.0ms (0.4%)

preprocess568.0ms (13.5%)

end0.0ms (0%)

Profiling