Metrics for bug333 (missed optimization)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
100%	50%	0%	50%	0%	0%	0%	1

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample1.5s (65.6%)

Memory

47.4MiB live, 1 444.6MiB allocated; 294ms collecting garbage

Samples

659.0ms	4 734×	1	valid
553.0ms	3 413×	2	valid
4.0ms	109×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 917.0ms

ival-sqrt: 425.0ms (46.4% of total)

adjust: 296.0ms (32.3% of total)

ival-add!: 105.0ms (11.5% of total)

ival-sub!: 91.0ms (9.9% of total)

Bogosity

preprocess110.0ms (4.7%)

Memory

-8.6MiB live, 33.8MiB allocated; 14ms collecting garbage

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	32
1	24	32
2	30	32
3	62	28
4	266	28
5	2403	28

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	7.8%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 16 to 14 computations (12.5% saved)

series5.0ms (0.2%)

Memory

11.1MiB live, 11.1MiB allocated; 0ms collecting garbage

Counts

7 → 41

Calls

Call 1

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

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#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 x)))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (- 1 x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (sqrt (/ -1 x)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (sqrt (/ -1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ -1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (sqrt (/ -1 x))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ -1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ -1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

Calls

3 calls:

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

Time

Variable

Point

Expression

2.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))

2.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))

1.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (sqrt (+ 1 x)) (+ 1 x) 1 x (sqrt (- 1 x)) (- 1 x))

rewrite195.0ms (8.3%)

Memory

24.0MiB live, 253.6MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	197	1243
0	203	1164
1	1108	1158
0	8264	1111

Stop Event

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

Counts

48 → 95

Calls

Call 1

Inputs
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal 1 binary64) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#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 x)))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* -1/2 x))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* -1/8 x) 1/2)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (+ 1 (* x (- (* x (- (* -1/16 x) 1/8)) 1/2)))))
#s(approx (- 1 x) #s(hole binary64 (+ 1 (* -1 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (sqrt (/ 1 x)))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x)))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))
#s(approx (+ 1 x) #s(hole binary64 (* x (+ 1 (/ 1 x)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (sqrt (/ -1 x)))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (+ (sqrt (/ -1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* x (- (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ -1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 x)))
#s(approx (- 1 x) #s(hole binary64 (* x (- (/ 1 x) 1))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (sqrt (/ 1 x))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ 1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ 1 x))))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))
#s(approx (sqrt (+ 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ 1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (sqrt (/ -1 x))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (+ (sqrt (/ -1 x)) (* 1/2 (/ 1 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))) (/ 1/8 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))))
#s(approx (sqrt (- 1 x)) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt (/ -1 x)) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))))))
#s(approx (- 1 x) #s(hole binary64 (* -1 (* x (- 1 (/ 1 x))))))

Outputs
(/.f64 (neg.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)))) (neg.f64 (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))))))
(/.f64 (-.f64 (+.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))))))
(-.f64 (/.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))) (/.f64 (-.f64 #s(literal 1 binary64) x) (+.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))) (/.f64 (.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) x) (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)))))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 #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)))
(exp.f64 (*.f64 (log.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (fabs.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(*.f64 (neg.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64)))) (neg.f64 (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))))
(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) #s(literal 2 binary64))
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64)))
(/.f64 (fma.f64 (.f64 x x) x #s(literal 1 binary64)) (fma.f64 x x (-.f64 #s(literal 1 binary64) (.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x)))) (/.f64 (.f64 (.f64 x x) x) (+.f64 #s(literal 1 binary64) (fma.f64 x x (neg.f64 x)))))
(+.f64 x #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(sqrt.f64 (-.f64 #s(literal 1 binary64) x))
(exp.f64 (*.f64 (log.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(*.f64 (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (fabs.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))) (neg.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x))))
(*.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(pow.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x))) (neg.f64 (+.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 #s(literal 1 binary64) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (+.f64 x #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 x #s(literal 1 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) x)) (+.f64 #s(literal 1 binary64) (fma.f64 x x (*.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))) (/.f64 (*.f64 x x) (+.f64 x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 (.f64 x x) x) (+.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 #s(literal 1 binary64) x)))))
(-.f64 #s(literal 1 binary64) x)
(sqrt.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64)) x))
#s(approx (sqrt (+ 1 x)) #s(literal 1 binary64))
#s(approx (sqrt (+ 1 x)) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal 1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (+ 1 x)) (fma.f64 (fma.f64 (fma.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) (+.f64 x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (fma.f64 (fma.f64 (fma.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) (+.f64 (neg.f64 x) #s(literal 1 binary64)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64)))))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (+.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (*.f64 x x)))))) x))
#s(approx (sqrt (+ 1 x)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) x))
#s(approx (sqrt (+ 1 x)) (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) x))
#s(approx (sqrt (+ 1 x)) (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (.f64 x x))))) x))
#s(approx (sqrt (+ 1 x)) (.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (*.f64 x x))))) x))
#s(approx (+ 1 x) (fma.f64 #s(literal 1 binary64) x #s(literal 1 binary64)))
#s(approx (sqrt (- 1 x)) (*.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) x))
#s(approx (sqrt (- 1 x)) (.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) x))
#s(approx (sqrt (- 1 x)) (.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (.f64 x x))))) x))
#s(approx (sqrt (- 1 x)) (.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (*.f64 x x)))))) x))
#s(approx (- 1 x) (neg.f64 x))
#s(approx (- 1 x) (*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (neg.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (*.f64 x x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64)))))) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (+.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (*.f64 x x))))))))
#s(approx (sqrt (+ 1 x)) (*.f64 (neg.f64 x) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))))
#s(approx (sqrt (+ 1 x)) (.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x)))))
#s(approx (sqrt (+ 1 x)) (.f64 (neg.f64 x) (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (.f64 x x)))))))
#s(approx (sqrt (+ 1 x)) (.f64 (neg.f64 x) (-.f64 (+.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x x) (*.f64 x x)))))))
#s(approx (sqrt (- 1 x)) (*.f64 (neg.f64 x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (*.f64 x x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x)))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (-.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (.f64 x x))) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (.f64 x x)))))))
#s(approx (sqrt (- 1 x)) (.f64 (neg.f64 x) (+.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (-.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))) (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal -1 binary64) x)) (.f64 x x)))) (/.f64 #s(literal 1/8 binary64) (.f64 (.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 (/.f64 #s(literal -1 binary64) x))) (.f64 (.f64 x x) (*.f64 x x))))))))
#s(approx (- 1 x) (*.f64 (neg.f64 x) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))

eval8.0ms (0.4%)

Memory: 13.0MiB live, 13.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 1 123 to 387 computations (65.5% saved)

prune3.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Accuracy

100.0%

Counts

91 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.8%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	100.0%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
▶	99.9%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
▶	99.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)

Compiler

Compiled 45 to 43 computations (4.4% saved)

series24.0ms (1%)

Memory

-36.9MiB live, 9.7MiB allocated; 3ms collecting garbage

Counts

13 → 31

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
x
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1/8 binary64)
#s(literal 1 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal 7/128 binary64)

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 (+ 1 (* 1/8 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 1/8))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 (+ 1/8 (* 7/128 (pow x 2)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (* (+ (* (* x x) 1/8) 1) x) #s(hole binary64 (* 1/8 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/8) 1) x) #s(hole binary64 (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 (* 1/8 (pow x 2))))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* 7/128 (pow x 5))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* 7/128 (pow x 4))))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 (* 7/128 (pow x 2))))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))))

Calls

3 calls:

Time	Variable		Point	Expression
20.0ms	x	@	inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) x (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 1/8) 1) x) (+ (* (* x x) 1/8) 1) (* x x) 1/8 1 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (+ (* 7/128 (* x x)) 1/8) 7/128)
2.0ms	x	@	-inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) x (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 1/8) 1) x) (+ (* (* x x) 1/8) 1) (* x x) 1/8 1 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (+ (* 7/128 (* x x)) 1/8) 7/128)
1.0ms	x	@	0	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) x (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 1/8) 1) x) (+ (* (* x x) 1/8) 1) (* x x) 1/8 1 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (+ (* 7/128 (* x x)) 1/8) 7/128)

Time

Variable

Point

Expression

20.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) x (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 1/8) 1) x) (+ (* (* x x) 1/8) 1) (* x x) 1/8 1 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (+ (* 7/128 (* x x)) 1/8) 7/128)

2.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) x (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 1/8) 1) x) (+ (* (* x x) 1/8) 1) (* x x) 1/8 1 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (+ (* 7/128 (* x x)) 1/8) 7/128)

1.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) x (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (* x x) 1/8) 1) x) (+ (* (* x x) 1/8) 1) (* x x) 1/8 1 (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (+ (* 7/128 (* x x)) 1/8) 7/128)

rewrite124.0ms (5.3%)

Memory

5.6MiB live, 157.7MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	152	1028
0	164	959
1	827	925
0	9277	892

Stop Event

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

Counts

44 → 273

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
x
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64))
(*.f64 x x)
#s(literal 1/8 binary64)
#s(literal 1 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
(.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x)
(fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (.f64 x x) #s(literal 1 binary64))
(fma.f64 #s(literal 7/128 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal 7/128 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 1))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 (+ 1 (* 1/8 (pow x 2)))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2)))))))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 1/8))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 (+ 1/8 (* 7/128 (pow x 2)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (* (+ (* (* x x) 1/8) 1) x) #s(hole binary64 (* 1/8 (pow x 3))))
#s(approx (* (+ (* (* x x) 1/8) 1) x) #s(hole binary64 (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 (* 1/8 (pow x 2))))
#s(approx (+ (* (* x x) 1/8) 1) #s(hole binary64 (* (pow x 2) (+ 1/8 (/ 1 (pow x 2))))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* 7/128 (pow x 5))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* (pow x 5) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* 7/128 (pow x 4))))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) #s(hole binary64 (* (pow x 4) (+ 7/128 (+ (* 1/8 (/ 1 (pow x 2))) (/ 1 (pow x 4)))))))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 (* 7/128 (pow x 2))))
#s(approx (+ (* 7/128 (* x x)) 1/8) #s(hole binary64 (* (pow x 2) (+ 7/128 (* 1/8 (/ 1 (pow x 2)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) #s(hole binary64 (* -1 (* (pow x 5) (- (* -1 (/ (+ 1/8 (/ 1 (pow x 2))) (pow x 2))) 7/128)))))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
x
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) x) (.f64 x x))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) x))
(.f64 (.f64 (.f64 x x) x) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(.f64 (.f64 x x) (.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 x (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1 binary64))) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -1 binary64)))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x)))) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) #s(literal 1 binary64))) (-.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 (.f64 x x) x) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (.f64 (.f64 (.f64 x x) x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal 1/512 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/64 binary64)))
(/.f64 (.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1 binary64)) x) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x))) x) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) #s(literal 1 binary64)) x) (-.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x) #s(literal 1 binary64)) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x)) #s(literal 1/512 binary64) #s(literal 1 binary64)) x) (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x))) (.f64 (.f64 x x) x)) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal 1/512 binary64)) (.f64 (.f64 x x) x)) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/64 binary64)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)))) (-.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) (.f64 x x)) (-.f64 (.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) x))
(/.f64 (fma.f64 (.f64 x x) x (pow.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) #s(literal 3 binary64))) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64))) (.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64))))))
(/.f64 (+.f64 (pow.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) #s(literal 3 binary64)) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) x))))
(fma.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) x)
(fma.f64 (.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) #s(literal 1 binary64) x)
(fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x)
(fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x x)
(fma.f64 (.f64 x x) (.f64 #s(literal 1/8 binary64) x) x)
(fma.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x)) x)
(fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x) x)
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/8 binary64)) x)
(-.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (.f64 (neg.f64 (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64)) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (*.f64 x x) x)))
(-.f64 x (.f64 (neg.f64 x) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(-.f64 x (.f64 (.f64 #s(literal -1/8 binary64) (*.f64 x x)) x))
(+.f64 (.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64)) x)
(+.f64 x (.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64)))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) x) x)
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64))))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (*.f64 x x))
(.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64)))
(.f64 x (.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64))))
(/.f64 (.f64 (.f64 x x) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x)))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal 1/512 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/64 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) x))) (.f64 x x)) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) x) (.f64 (.f64 x x) x))) #s(literal 1/512 binary64)) (.f64 x x)) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/64 binary64)))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x) (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/8 binary64) (.f64 x x))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/64 binary64) (.f64 (.f64 (.f64 x x) x) x) #s(literal -1 binary64))) (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal -1 binary64))))
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#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (.f64 x x) x) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (*.f64 x x) x) x))))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (-.f64 (+.f64 (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64)))))) (/.f64 #s(literal -1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (.f64 x x) x) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))))) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (*.f64 x x) x) x)))) x))
#s(approx (* (+ (* (* x x) 1/8) 1) x) (.f64 (.f64 (*.f64 x x) x) #s(literal 1/8 binary64)))
#s(approx (* (+ (* (* x x) 1/8) 1) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (+ (* (* x x) 1/8) 1) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
#s(approx (+ (* (* x x) 1/8) 1) (fma.f64 (*.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (*.f64 (pow.f64 x #s(literal 5 binary64)) #s(literal 7/128 binary64)))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (.f64 (-.f64 #s(literal 7/128 binary64) (/.f64 #s(literal -1/8 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (*.f64 x x)) #s(literal 7/128 binary64)) (pow.f64 x #s(literal 5 binary64))))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (.f64 (.f64 (.f64 (.f64 x x) #s(literal 7/128 binary64)) x) x))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (.f64 (.f64 (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)) x) x))
#s(approx (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) (.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) #s(literal 7/128 binary64)) (.f64 (.f64 (.f64 x x) x) x)))
#s(approx (+ (* 7/128 (* x x)) 1/8) (.f64 (.f64 x x) #s(literal 7/128 binary64)))
#s(approx (+ (* 7/128 (* x x)) 1/8) (fma.f64 (*.f64 x x) #s(literal 7/128 binary64) #s(literal 1/8 binary64)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (neg.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (+.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (.f64 x x) x) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (*.f64 x x) x) x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (-.f64 (+.f64 (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64)))))) (/.f64 #s(literal -1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (.f64 x x) x) x)))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))))) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 (*.f64 x x) x) x))))))
#s(approx (* (+ (* (+ (* 7/128 (* x x)) 1/8) (* x x)) 1) x) (.f64 (neg.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (*.f64 (neg.f64 x) x)) #s(literal 7/128 binary64))) (pow.f64 x #s(literal 5 binary64))))

eval28.0ms (1.2%)

Memory: 18.9MiB live, 63.2MiB allocated; 4ms collecting garbage
Compiler: Compiled 3 057 to 1 134 computations (62.9% saved)

prune6.0ms (0.3%)

Memory

12.2MiB live, 12.2MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	272	1	273
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	273	4	277

Accuracy

100.0%

Counts

277 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.8%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
▶	99.9%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x))
✓	100.0%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
✓	99.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)

Compiler

Compiled 44 to 42 computations (4.5% saved)

series11.0ms (0.5%)

Memory

-50.9MiB live, 8.5MiB allocated; 8ms collecting garbage

Counts

6 → 16

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x)
(.f64 (.f64 x x) x)
(*.f64 x x)
x
#s(literal 1/8 binary64)

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (+ (* (* (* x x) x) 1/8) x) #s(hole binary64 (* 1/8 (pow x 3))))
#s(approx (+ (* (* (* x x) x) 1/8) x) #s(hole binary64 (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))))

Calls

3 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (* (* x x) x) 1/8) x) (* (* x x) x) (* x x) x 1/8)
1.0ms	x	@	-inf	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (* (* x x) x) 1/8) x) (* (* x x) x) (* x x) x 1/8)
1.0ms	x	@	0	((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (* (* x x) x) 1/8) x) (* (* x x) x) (* x x) x 1/8)

Time

Variable

Point

Expression

8.0ms

inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (* (* x x) x) 1/8) x) (* (* x x) x) (* x x) x 1/8)

1.0ms

-inf

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (* (* x x) x) 1/8) x) (* (* x x) x) (* x x) x 1/8)

1.0ms

((- (sqrt (+ 1 x)) (sqrt (- 1 x))) (+ (* (* (* x x) x) 1/8) x) (* (* x x) x) (* x x) x 1/8)

rewrite143.0ms (6.1%)

Memory

29.4MiB live, 167.0MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	109	652
0	115	603
1	622	580
0	7809	561

Stop Event

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

Counts

22 → 96

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x))
(fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x)
(.f64 (.f64 x x) x)
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* 1/8 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* 7/128 (pow x 2))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (+ 1 (* (pow x 2) (+ 1/8 (* (pow x 2) (+ 7/128 (* 33/1024 (pow x 2))))))))))
#s(approx (* (* x x) x) #s(hole binary64 (pow x 3)))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (+ (* (* (* x x) x) 1/8) x) #s(hole binary64 (* 1/8 (pow x 3))))
#s(approx (+ (* (* (* x x) x) 1/8) x) #s(hole binary64 (* (pow x 3) (+ 1/8 (/ 1 (pow x 2))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (sqrt (/ 1 x)) (sqrt (/ -1 x)))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ 1 x))))) (+ (sqrt (/ -1 x)) (/ 1/2 (* (pow x 2) (sqrt (/ -1 x))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3)))))) (+ (sqrt (/ -1 x)) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3)))))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) #s(hole binary64 (* -1 (* x (- (+ (sqrt (/ 1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ 1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ 1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ -1 x)) 3))))))) (+ (sqrt (/ -1 x)) (+ (/ 1/16 (* (pow x 6) (pow (sqrt (/ -1 x)) 5))) (+ (/ 1/2 (* (pow x 2) (sqrt (/ -1 x)))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt (/ 1 x)) 3))))))))))))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 x x)) x)
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) x) (.f64 x x))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (.f64 (pow.f64 x #s(literal 3/2 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1/8 binary64))))
(.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) x))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x)
(.f64 (.f64 x x) (.f64 x (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64))))
(.f64 (.f64 (.f64 x x) x) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64)))
(.f64 x (.f64 (.f64 x x) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/8 binary64))))
(.f64 x (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (.f64 x (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1 binary64))) (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (.f64 (.f64 x x) x) (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (.f64 (.f64 (.f64 x x) x) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))) #s(literal 1/512 binary64))) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/64 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) (.f64 x x)))) x) (-.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1 binary64)) x) (fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) (-.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 x x) x)) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x))) #s(literal 1/512 binary64)) (.f64 (.f64 x x) x)) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/8 binary64)) #s(literal 1/64 binary64)))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64))) (-.f64 x (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 x x))) (neg.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x) x)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal 3 binary64)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x))) (neg.f64 (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x))))))
(/.f64 (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 x x)) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x) x))
(/.f64 (fma.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal 3 binary64)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x)) (fma.f64 x x (-.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x) x))))
(/.f64 (fma.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal 3 binary64)) #s(literal 1/512 binary64) (.f64 (.f64 x x) x)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x)))))
(fma.f64 (*.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 x x) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (*.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/8 binary64)) x)
(fma.f64 (fabs.f64 x) (.f64 (fabs.f64 x) (.f64 #s(literal 1/8 binary64) x)) x)
(fma.f64 (neg.f64 x) (.f64 (neg.f64 x) (.f64 #s(literal 1/8 binary64) x)) x)
(fma.f64 (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x) #s(literal 1 binary64) x)
(fma.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x x)
(fma.f64 (.f64 x x) (.f64 #s(literal 1/8 binary64) x) x)
(fma.f64 #s(literal 1/8 binary64) (.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) x)) x)
(fma.f64 #s(literal 1/8 binary64) (.f64 (.f64 x x) x) x)
(fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x)
(fma.f64 x (.f64 (.f64 x x) #s(literal 1/8 binary64)) x)
(-.f64 (/.f64 (.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64)) (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x) x)) (/.f64 (.f64 x x) (-.f64 (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x) x)))
(-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x) (.f64 (neg.f64 (.f64 (.f64 x x) x)) (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x) (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) (.f64 (*.f64 x x) x)))
(-.f64 x (.f64 (neg.f64 x) (.f64 (*.f64 x x) #s(literal 1/8 binary64))))
(-.f64 x (.f64 (.f64 #s(literal -1/8 binary64) (*.f64 x x)) x))
(-.f64 x (.f64 (.f64 (neg.f64 x) x) (*.f64 #s(literal 1/8 binary64) x)))
(-.f64 x (.f64 #s(literal -1/8 binary64) (.f64 (*.f64 x x) x)))
(-.f64 x (.f64 (neg.f64 (.f64 (*.f64 x x) x)) #s(literal 1/8 binary64)))
(+.f64 (/.f64 (.f64 (pow.f64 (.f64 (.f64 x x) x) #s(literal 3 binary64)) #s(literal 1/512 binary64)) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 (.f64 x x) #s(literal 1/8 binary64)) x))))) (/.f64 (.f64 (.f64 x x) x) (fma.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x x)) #s(literal 1/64 binary64) (.f64 x (-.f64 x (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x))))))
(+.f64 (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x) x)
(+.f64 x (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x))
(.f64 (.f64 x (fabs.f64 x)) (fabs.f64 x))
(*.f64 (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))) (fabs.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (pow.f64 x #s(literal 3/2 binary64))))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 (.f64 (neg.f64 x) x) (neg.f64 x))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) x))
(.f64 (neg.f64 x) (.f64 (neg.f64 x) x))
(.f64 (.f64 x x) x)
(.f64 x (.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 x #s(literal 3 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
x
#s(literal 1/8 binary64)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 (fma.f64 (fma.f64 #s(literal 33/1024 binary64) (.f64 x x) #s(literal 7/128 binary64)) (.f64 x x) #s(literal 1/8 binary64)) x) x #s(literal 1 binary64)) x))
#s(approx (* (* x x) x) (.f64 (.f64 x x) x))
#s(approx (* x x) (*.f64 x x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (+.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (*.f64 x x)))))) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (-.f64 (-.f64 (+.f64 (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64)))))) (/.f64 #s(literal -1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))))) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (*.f64 x x))))) x))
#s(approx (+ (* (* (* x x) x) 1/8) x) (.f64 (.f64 (*.f64 x x) #s(literal 1/8 binary64)) x))
#s(approx (+ (* (* (* x x) x) 1/8) x) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (*.f64 (neg.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x)))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (+.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (*.f64 x x))))))))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (neg.f64 x) (-.f64 (-.f64 (+.f64 (-.f64 (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64)))))) (/.f64 #s(literal -1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (fma.f64 (/.f64 (/.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (sqrt.f64 x) (/.f64 #s(literal 1/16 binary64) (exp.f64 (fma.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 5 binary64) (.f64 (log.f64 x) #s(literal 6 binary64))))))) (/.f64 #s(literal 1/8 binary64) (.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (sqrt.f64 x)) (.f64 (.f64 x x) (*.f64 x x)))))))

eval13.0ms (0.6%)

Memory: -29.8MiB live, 23.1MiB allocated; 4ms collecting garbage
Compiler: Compiled 950 to 369 computations (61.2% saved)

prune3.0ms (0.1%)

Memory

5.4MiB live, 5.4MiB allocated; 0ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	88	4	92

Accuracy

100.0%

Counts

92 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	7.8%	(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
✓	99.9%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x))
✓	100.0%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))
✓	99.6%	#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)

Compiler

Compiled 85 to 69 computations (18.8% saved)

regimes4.0ms (0.2%)

Memory

10.7MiB live, 10.7MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (fma.f64 #s(literal 7/128 binary64) (.f64 x x) #s(literal 1/8 binary64)) (*.f64 x x) #s(literal 1 binary64)) x))

Calls

2 calls:

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

Results

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes3.0ms (0.1%)

Memory

7.3MiB live, 7.3MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x))
(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (fma.f64 (.f64 (.f64 x x) x) #s(literal 1/8 binary64) x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
99.9%	1	`x`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes2.0ms (0.1%)

Memory

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

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) (.f64 (fma.f64 (.f64 x x) #s(literal 1/8 binary64) #s(literal 1 binary64)) x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`(-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))`
99.9%	1	`x`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes2.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)

Outputs
#s(approx (- (sqrt (+ 1 x)) (sqrt (- 1 x))) x)

Calls

2 calls:

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

Results

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

derivations96.0ms (4.1%)

Memory

-37.3MiB live, 57.2MiB allocated; 3ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 35 to 22 computations (37.1% saved)

preprocess24.0ms (1%)

Memory: 28.5MiB live, 28.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 43 to 29 computations (32.6% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.5s (65.6%)

preprocess110.0ms (4.7%)

series5.0ms (0.2%)

rewrite195.0ms (8.3%)

eval8.0ms (0.4%)

prune3.0ms (0.1%)

series24.0ms (1%)

rewrite124.0ms (5.3%)

eval28.0ms (1.2%)

prune6.0ms (0.3%)

series11.0ms (0.5%)

rewrite143.0ms (6.1%)

eval13.0ms (0.6%)

prune3.0ms (0.1%)

regimes4.0ms (0.2%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

regimes2.0ms (0.1%)

derivations96.0ms (4.1%)

preprocess24.0ms (1%)

end0.0ms (0%)

Profiling