Metrics for sqrt times

start0.0ms (0%)

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

analyze1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	50%	0%	0%	50%	0%	2
50%	25%	25%	0%	0%	50%	0%	3
66.7%	25%	12.5%	0%	0%	62.5%	0%	4
80%	25%	6.2%	0%	0%	68.7%	0%	5
88.9%	25%	3.1%	0%	0%	71.8%	0%	6
94.1%	25%	1.6%	0%	0%	73.4%	0%	7
97%	25%	0.8%	0%	0%	74.2%	0%	8
98.5%	25%	0.4%	0%	0%	74.6%	0%	9
99.2%	25%	0.2%	0%	0%	74.8%	0%	10
99.6%	25%	0.1%	0%	0%	74.9%	0%	11
99.8%	25%	0%	0%	0%	74.9%	0%	12

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample926.0ms (22.4%)

Memory

28.5MiB live, 714.9MiB allocated; 861ms collecting garbage

Samples

656.0ms	8 251×	0	valid
1.0ms	15×	0	invalid
0.0ms	5×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 512.0ms

ival-mult: 331.0ms (64.6% of total)

ival-sqrt: 111.0ms (21.7% of total)

ival-sub: 54.0ms (10.5% of total)

ival-true: 5.0ms (1% of total)

exact: 5.0ms (1% of total)

ival-assert: 3.0ms (0.6% of total)

adjust: 2.0ms (0.4% of total)

Bogosity

explain73.0ms (1.8%)

Memory

22.3MiB live, 112.5MiB allocated; 35ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
-	-	`(sqrt.f64 (-.f64 x #s(literal 1 binary64)))`
-	-	`(sqrt.f64 x)`
-	-	`(-.f64 x #s(literal 1 binary64))`
-	-	`#s(literal 1 binary64)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

41.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-sub: 14.0ms (46.2% of total)

ival-sqrt: 12.0ms (39.6% of total)

ival-mult: 3.0ms (9.9% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess17.0ms (0.4%)

Memory

-19.3MiB live, 27.5MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	19
1	15	19
2	17	19
0	6	7
0	10	7
1	13	7
0	13	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

5.9MiB live, 5.9MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 x)
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
cost-diff	0	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	10	18
1	13	18
0	13	18

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.4%)

Memory

31.5MiB live, 31.5MiB allocated; 0ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x #s(literal 1 binary64))
accuracy	0.0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.0	(sqrt.f64 x)
accuracy	0.50390625	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Samples

12.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-sqrt: 3.0ms (45.9% of total)

ival-sub: 1.0ms (15.3% of total)

ival-mult: 1.0ms (15.3% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

-50.8MiB live, 6.5MiB allocated; 4ms collecting garbage

Counts

4 → 28

Calls

Call 1

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

Outputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- x 1)
(sqrt x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* 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))))))))
(* x (- 1 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))
(* -1 (* x (- (/ 1 x) 1)))

Calls

3 calls:

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

simplify138.0ms (3.3%)

Memory

17.1MiB live, 107.9MiB allocated; 10ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	150	457
1	495	390
2	2202	378
3	7444	375
0	8362	345

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 27

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
-1
(- x 1)
(sqrt x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* 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))))))))
(* x (- 1 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))
(* -1 (* x (- (/ 1 x) 1)))

Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (.f64 (/.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) (sqrt.f64 x))) (sqrt.f64 #s(literal -1 binary64))) x) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64)) x (/.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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))))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* x (- 1 (/ 1 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 x x) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)) x)
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -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))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -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)))))))
(*.f64 (fma.f64 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(* -1 (* x (- (/ 1 x) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))

rewrite223.0ms (5.4%)

Memory

44.2MiB live, 175.7MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	10	15
1	32	15
2	148	15
3	1189	15
0	9614	13

Stop Event

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

Counts

4 → 354

Calls

Call 1

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

Outputs
(.f64 (.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))) (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))))
(.f64 (.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
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(fma.f64 #s(literal 1 binary64) (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal 1 binary64) (neg.f64 x) #s(literal -1 binary64))
(fma.f64 x (/.f64 (*.f64 x x) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(fma.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(fma.f64 x #s(literal -1 binary64) #s(literal -1 binary64))
(expm1.f64 (/.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(expm1.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(expm1.f64 (log.f64 x))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (/.f64 (pow.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 (*.f64 x x) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (/.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -2 binary64)) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -3 binary64)) (+.f64 (pow.f64 (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) (.f64 (.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))))) (/.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))))))
(-.f64 (/.f64 (fma.f64 x x (pow.f64 x #s(literal 3 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))) (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 #s(literal 1 binary64) x)) (/.f64 (pow.f64 (+.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 (pow.f64 (+.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (*.f64 (neg.f64 (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (.f64 (neg.f64 (.f64 x x)) x) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(-.f64 (/.f64 x #s(literal 1 binary64)) #s(literal 1 binary64))
(-.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 x x) (-.f64 x #s(literal 1 binary64))))
(-.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (pow.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 (neg.f64 x) #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))
(exp.f64 (log.f64 (-.f64 x #s(literal 1 binary64))))
(+.f64 (/.f64 (*.f64 x x) (neg.f64 (-.f64 x #s(literal 1 binary64)))) (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))))
(+.f64 (cosh.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))) (sinh.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))))
(+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 (neg.f64 x)) (neg.f64 x)) (-.f64 x #s(literal 1 binary64))))
(+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 (neg.f64 x) x) (-.f64 x #s(literal 1 binary64))))
(+.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (*.f64 x (neg.f64 x)) (-.f64 x #s(literal 1 binary64))))
(+.f64 #s(literal -1 binary64) (neg.f64 x))
(+.f64 (*.f64 x (/.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 x #s(literal 1 binary64)) x #s(literal 1 binary64)))))
(+.f64 (neg.f64 x) #s(literal -1 binary64))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))) (neg.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 (neg.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 x) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 x))
(pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (cosh.f64 (log.f64 (sqrt.f64 x)))) (.f64 (sinh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))) (-.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (log.f64 (sqrt.f64 x))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (cosh.f64 (log.f64 (sqrt.f64 x))) (-.f64 (.f64 (sinh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x)))) (.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x)))))))
(sqrt.f64 x)
(fabs.f64 (sqrt.f64 x))
(exp.f64 (fma.f64 (log.f64 x) #s(literal 1/4 binary64) (*.f64 (log.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))

eval67.0ms (1.6%)

Memory: -32.6MiB live, 56.9MiB allocated; 8ms collecting garbage
Compiler: Compiled 7 786 to 1 459 computations (81.3% saved)

prune6.0ms (0.1%)

Memory

19.8MiB live, 19.8MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	374	4	378
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	374	5	379

Accuracy

100.0%

Counts

379 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.8%	(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	99.4%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
▶	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
▶	97.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 65 to 49 computations (24.6% saved)

simplify91.0ms (2.2%)

Memory

-4.8MiB live, 95.6MiB allocated; 19ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
cost-diff	0	(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)
cost-diff	0	(sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x))
cost-diff	0	(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
cost-diff	0	(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
cost-diff	0	(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
cost-diff	3	(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
cost-diff	0	(/.f64 #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
cost-diff	3	(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	156
0	45	156
1	68	156
2	108	148
3	209	144
4	428	144
5	1447	144
6	3909	144
0	8280	144

Stop Event

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

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
#s(literal -1/2 binary64)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
x
#s(literal -1/8 binary64)
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(-.f64 x #s(literal 1/2 binary64))
(/.f64 #s(literal -1/2 binary64) x)
#s(literal -1/2 binary64)
x
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (+.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(+.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
#s(literal -1/2 binary64)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
x
#s(literal -1/8 binary64)
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))

localize64.0ms (1.5%)

Memory

24.8MiB live, 113.5MiB allocated; 14ms collecting garbage

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
accuracy	0.0625	(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)
accuracy	18.250508391099967	(sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x))
accuracy	19.336371042296403	(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
accuracy	0.0	(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
accuracy	0.03515625	(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
accuracy	0.0390625	(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
accuracy	0.3807888781465246	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
accuracy	0.0	(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
accuracy	0.0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	0.695706275433649	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
accuracy	1.5983383903421902	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Samples

49.0ms

256×

valid

Compiler

Compiled 136 to 27 computations (80.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-div: 12.0ms (32.4% of total)

ival-sub: 9.0ms (24.3% of total)

ival-mult: 6.0ms (16.2% of total)

ival-sqrt: 5.0ms (13.5% of total)

ival-add: 2.0ms (5.4% of total)

ival-pow2: 2.0ms (5.4% of total)

exact: 1.0ms (2.7% of total)

adjust: 0.0ms (0% of total)

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

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

series56.0ms (1.4%)

Memory

-39.8MiB live, 28.6MiB allocated; 28ms collecting garbage

Counts

14 → 75

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(/.f64 #s(literal -1/2 binary64) x)
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))

Outputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
-1/2
(- x 1/2)
(/ -1/2 x)
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/ -1/16 (pow x 3))
(/ (- (* -1/8 x) 1/16) (pow x 3))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 3))
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(sqrt x)
(+ (sqrt x) (* -1 (sqrt (pow x 3))))
x
(* x (+ 1 (* -2 x)))
(* x (+ 1 (* x (- x 2))))
1
(+ 1 (* -2 x))
(+ 1 (* x (- x 2)))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)
(* -1 (+ 1/2 (* 1/8 (/ 1 x))))
(- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)
(* -1 x)
(* x (- (* 1/2 (/ 1 x)) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(* -1 (sqrt (pow x 3)))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(pow x 3)
(* (pow x 3) (- 1 (* 2 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* 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))))))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (pow x 3) (- (* 2 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 2) x)) 1)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))

Calls

3 calls:

Time	Variable		Point	Expression
50.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (+ (* (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (/ (- (/ 1/16 x) -1/8) x) (sqrt (- x 1)))
3.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (+ (* (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (/ (- (/ 1/16 x) -1/8) x) (sqrt (- x 1)))
2.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (+ (* (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (/ (- (/ 1/16 x) -1/8) x) (sqrt (- x 1)))

Time

Variable

Point

Expression

50.0ms

((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (+ (* (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (/ (- (/ 1/16 x) -1/8) x) (sqrt (- x 1)))

3.0ms

inf

((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (+ (* (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (/ (- (/ 1/16 x) -1/8) x) (sqrt (- x 1)))

2.0ms

-inf

((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (+ (* (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) x) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (/ (- (/ 1/16 x) -1/8) x) (sqrt (- x 1)))

simplify183.0ms (4.4%)

Memory

18.5MiB live, 204.8MiB allocated; 41ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	257	955
1	844	840
2	3507	828
0	8227	788

Stop Event

1×	iter limit
1×	node limit

Counts

75 → 74

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
-1/2
(- x 1/2)
(/ -1/2 x)
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/ -1/16 (pow x 3))
(/ (- (* -1/8 x) 1/16) (pow x 3))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 3))
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(sqrt x)
(+ (sqrt x) (* -1 (sqrt (pow x 3))))
x
(* x (+ 1 (* -2 x)))
(* x (+ 1 (* x (- x 2))))
1
(+ 1 (* -2 x))
(+ 1 (* x (- x 2)))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(sqrt -1)
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))
(/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)
(* -1 (+ 1/2 (* 1/8 (/ 1 x))))
(- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)
(* -1 x)
(* x (- (* 1/2 (/ 1 x)) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(* -1 (sqrt (pow x 3)))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(pow x 3)
(* (pow x 3) (- 1 (* 2 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(* 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))))))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (pow x 3) (- (* 2 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 2) x)) 1)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -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))))))
(* -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)))))))

Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
(/ -1/2 x)
(/.f64 #s(literal -1/2 binary64) x)
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/.f64 (/.f64 (-.f64 (*.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64)) x) x)
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/.f64 (/.f64 (-.f64 (.f64 (-.f64 (.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)) x) #s(literal 1/16 binary64)) x) x)
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/.f64 (/.f64 (-.f64 (.f64 (-.f64 (.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) x) #s(literal 1/16 binary64)) x) x)
(/ -1/16 (pow x 3))
(/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (- (* -1/8 x) 1/16) (pow x 3))
(/.f64 (fma.f64 #s(literal -1/8 binary64) x #s(literal -1/16 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 3))
(/.f64 (fma.f64 (-.f64 (*.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)) x #s(literal -1/16 binary64)) (pow.f64 x #s(literal 3 binary64)))
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 (sqrt.f64 x) (-.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal -1 binary64)))) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 #s(literal 0 binary64) x #s(literal -1/2 binary64))) x)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1 (sqrt (pow x 3))))
(-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
x
(* x (+ 1 (* -2 x)))
(*.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (- x 2))))
(*.f64 (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- x 2)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (/.f64 (fma.f64 #s(literal 1/8 binary64) x #s(literal 1/16 binary64)) x) x)
(sqrt -1)
(sqrt.f64 #s(literal -1 binary64))
(+ (sqrt -1) (* 1/2 (/ x (sqrt -1))))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) x (sqrt.f64 #s(literal -1 binary64)))
(+ (sqrt -1) (* x (+ (* -1/8 (/ x (pow (sqrt -1) 3))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (/.f64 x (sqrt.f64 #s(literal -1 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)))
(+ (sqrt -1) (* x (+ (* x (- (* 1/16 (/ x (pow (sqrt -1) 5))) (* 1/8 (/ 1 (pow (sqrt -1) 3))))) (* 1/2 (/ 1 (sqrt -1))))))
(fma.f64 (fma.f64 (-.f64 (*.f64 (/.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) #s(literal 1/16 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) x (sqrt.f64 #s(literal -1 binary64)))
(* x (- 1 (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) x x)
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x)
(/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
(* -1 (+ 1/2 (* 1/8 (/ 1 x))))
(-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x))
(- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(* -1 x)
(neg.f64 x)
(* x (- (* 1/2 (/ 1 x)) 1))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)) x)
(* -1 (sqrt (pow x 3)))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (- 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(*.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(*.f64 x (fma.f64 (/.f64 #s(literal -2 binary64) x) x x))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(*.f64 x (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x) x x))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(* x (+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3))))))
(*.f64 (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* x (+ (sqrt (/ 1 x)) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* -1/8 (sqrt (/ 1 (pow x 5)))))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (fma.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* 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))))))))
(.f64 (+.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -1/16 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) x x)
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x) x x)
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
(* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(*.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) x) #s(literal 1/2 binary64)) x) #s(literal 1 binary64)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(*.f64 (-.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)) x)
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
(* -1 (* (pow x 3) (- (* 2 (/ 1 x)) 1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 2) x)) 1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (neg.f64 x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) x) x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -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))))))
(.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(* -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)))))))
(.f64 (fma.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) #s(literal -1/16 binary64) (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))))))) #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)

rewrite251.0ms (6.1%)

Memory

-16.6MiB live, 172.4MiB allocated; 23ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	132
0	45	128
1	166	125
2	1012	116
0	9308	114

Stop Event

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

Counts

14 → 327

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(/.f64 #s(literal -1/2 binary64) x)
(fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
(/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x))
(*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)
(pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)) x)
(*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) x)
(*.f64 (-.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 x #s(literal 1/2 binary64)))
(.f64 x (.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))))
(*.f64 x (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)))
(*.f64 x (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (*.f64 x (-.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (*.f64 x (+.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (-.f64 (+.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal -1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) x))) (.f64 (/.f64 (.f64 x x) (-.f64 #s(literal -1/2 binary64) x)) (/.f64 (.f64 x x) (-.f64 #s(literal -1/2 binary64) x)))) (+.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) x)) (/.f64 (*.f64 x x) (-.f64 #s(literal -1/2 binary64) x))))
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(/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (neg.f64 x))
(/.f64 (-.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64))) (neg.f64 (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) #s(literal -1/512 binary64))) (neg.f64 (*.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)) x)))
(/.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) x) x (.f64 (neg.f64 x) #s(literal -1/8 binary64))) (.f64 x x))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) #s(literal -1/512 binary64)) (*.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)) x))
(/.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))) (neg.f64 x))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(neg.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) (neg.f64 x)))
(-.f64 (/.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 (pow.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 2 binary64)) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(-.f64 (/.f64 (/.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) x))))) (/.f64 (pow.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) #s(literal 2 binary64)) (.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) x))))))
(-.f64 (/.f64 (.f64 (/.f64 #s(literal 1/16 binary64) x) x) (.f64 x x)) (/.f64 (.f64 x #s(literal -1/8 binary64)) (.f64 x x)))
(-.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (/.f64 #s(literal 1/64 binary64) (.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(-.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)) x)) (/.f64 #s(literal -1/512 binary64) (.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)) x)))
(-.f64 (/.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) x) (/.f64 (/.f64 #s(literal -1/64 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) x))
(-.f64 (/.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) x) (/.f64 (/.f64 #s(literal -1/512 binary64) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) x))
(-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) x) (/.f64 #s(literal -1/8 binary64) x))
(*.f64 (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.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 (exp.f64 (log.f64 (-.f64 x #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (-.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sinh.f64 (acosh.f64 x))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3/2 binary64))))) (neg.f64 (sqrt.f64 (+.f64 (fma.f64 x x x) #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (sqrt.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (fma.f64 x x x) #s(literal 1 binary64)))))
(/.f64 (sinh.f64 (acosh.f64 x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sinh.f64 (acosh.f64 (pow.f64 x #s(literal 3/2 binary64)))) (sqrt.f64 (+.f64 (fma.f64 x x x) #s(literal 1 binary64))))
(neg.f64 (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 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 (cosh.f64 (.f64 (log.f64 (-.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (-.f64 x #s(literal 1 binary64))) #s(literal 1/2 binary64))))

eval65.0ms (1.6%)

Memory: -0.6MiB live, 85.0MiB allocated; 15ms collecting garbage
Compiler: Compiled 12 310 to 1 776 computations (85.6% saved)

prune7.0ms (0.2%)

Memory

24.4MiB live, 24.4MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	388	3	391
Fresh	0	0	0
Picked	3	1	4
Done	0	1	1
Total	391	5	396

Accuracy

100.0%

Counts

396 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.8%	(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	99.4%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
▶	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 67 to 53 computations (20.9% saved)

simplify77.0ms (1.9%)

Memory

0.4MiB live, 45.5MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)
cost-diff	0	(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))
cost-diff	0	(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
cost-diff	0	(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
cost-diff	0	(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
cost-diff	1	(fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x)
cost-diff	0	(-.f64 x #s(literal 1/2 binary64))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	157
0	44	155
1	58	155
2	84	155
3	142	155
4	312	155
5	409	155
6	502	155
7	632	155
8	963	155
9	1378	155
10	1851	155
11	3000	155
12	3180	155
13	3388	155
14	3881	155
15	3890	155
16	3912	155
17	4000	155
18	4028	155
0	4028	155

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
(fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
#s(literal -1/2 binary64)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
x
#s(literal -1/8 binary64)
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(-.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
x
#s(literal 1/2 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (-.f64 #s(literal 1/2 binary64) x)))
(fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x)
(-.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (-.f64 #s(literal 1/2 binary64) x))
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(-.f64 (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) #s(literal 1/2 binary64))
#s(literal -1/2 binary64)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
x
#s(literal -1/8 binary64)
#s(literal 1 binary64)
(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(-.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(literal 1 binary64)
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))

localize96.0ms (2.3%)

Memory

-14.4MiB live, 94.3MiB allocated; 8ms collecting garbage

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0	#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
accuracy	0.0625	(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)
accuracy	18.250508391099967	(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))
accuracy	19.336371042296403	(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
accuracy	0.0	(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
accuracy	0.0	(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
accuracy	0.0390625	(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
accuracy	0.3807888781465246	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
accuracy	0.0	(-.f64 x #s(literal 1/2 binary64))
accuracy	0.695706275433649	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))

Samples

65.0ms

256×

valid

Compiler

Compiled 116 to 28 computations (75.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-sub: 12.0ms (36.4% of total)

ival-mult: 6.0ms (18.2% of total)

ival-sqrt: 5.0ms (15.2% of total)

ival-div: 4.0ms (12.1% of total)

ival-add: 2.0ms (6.1% of total)

ival-pow2: 2.0ms (6.1% of total)

exact: 1.0ms (3% of total)

adjust: 0.0ms (0% of total)

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

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

series3.0ms (0.1%)

Memory

7.1MiB live, 7.1MiB allocated; 0ms collecting garbage

Counts

11 → 61

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))

Outputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
-1/2
(- x 1/2)
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(sqrt x)
(+ (sqrt x) (* -1 (sqrt (pow x 3))))
x
(* x (+ 1 (* -2 x)))
(* x (+ 1 (* x (- x 2))))
1
(+ 1 (* -2 x))
(+ 1 (* x (- x 2)))
(/ 1/16 x)
(/ (+ 1/16 (* 1/8 x)) x)
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (+ 1/2 (* 1/8 (/ 1 x))))
(- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(* -1 x)
(* x (- (* 1/2 (/ 1 x)) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(* -1 (sqrt (pow x 3)))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(pow x 3)
(* (pow x 3) (- 1 (* 2 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
1/8
(+ 1/8 (* 1/16 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (pow x 3) (- (* 2 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 2) x)) 1)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

((* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (+ (* (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) 1) x) (* (sqrt (- x 1)) (sqrt x)) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (- (/ 1/16 x) -1/8) x) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (- (/ 1/16 x) -1/8))

1.0ms

-inf

((* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (+ (* (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) 1) x) (* (sqrt (- x 1)) (sqrt x)) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (- (/ 1/16 x) -1/8) x) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (- (/ 1/16 x) -1/8))

1.0ms

inf

((* (sqrt (- x 1)) (sqrt x)) (- x 1/2) (+ (* (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) 1) x) (* (sqrt (- x 1)) (sqrt x)) (- -1/2 (/ (- (/ 1/16 x) -1/8) x)) (/ (- (/ 1/16 x) -1/8) x) (/ (sqrt (* (pow (- 1 x) 2) x)) (sqrt (- x 1))) (sqrt (* (pow (- 1 x) 2) x)) (* (pow (- 1 x) 2) x) (pow (- 1 x) 2) (- (/ 1/16 x) -1/8))

simplify175.0ms (4.2%)

Memory

7.7MiB live, 194.8MiB allocated; 45ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	202	655
1	658	591
2	2630	512
0	8834	497

Stop Event

1×	iter limit
1×	node limit

Counts

61 → 60

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
-1/2
(- x 1/2)
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(sqrt x)
(+ (sqrt x) (* -1 (sqrt (pow x 3))))
x
(* x (+ 1 (* -2 x)))
(* x (+ 1 (* x (- x 2))))
1
(+ 1 (* -2 x))
(+ 1 (* x (- x 2)))
(/ 1/16 x)
(/ (+ 1/16 (* 1/8 x)) x)
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(* -1 (+ 1/2 (* 1/8 (/ 1 x))))
(- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(* -1 x)
(* x (- (* 1/2 (/ 1 x)) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(* -1 (sqrt (pow x 3)))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(pow x 3)
(* (pow x 3) (- 1 (* 2 (/ 1 x))))
(* (pow x 3) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(pow x 2)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
1/8
(+ 1/8 (* 1/16 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* (pow x 3) (- (* 2 (/ 1 x)) 1)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 2) x)) 1)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))

Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(/.f64 (-.f64 (.f64 (-.f64 (.f64 (-.f64 x #s(literal 1/2 binary64)) x) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(*.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x)))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1 (sqrt (pow x 3))))
(-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
x
(* x (+ 1 (* -2 x)))
(*.f64 (fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64)) x)
(* x (+ 1 (* x (- x 2))))
(*.f64 (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- x 2)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(/ 1/16 x)
(/.f64 #s(literal 1/16 binary64) x)
(/ (+ 1/16 (* 1/8 x)) x)
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (+ 1/2 (* 1/8 (/ 1 x))))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2)
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(* -1 x)
(neg.f64 x)
(* x (- (* 1/2 (/ 1 x)) 1))
(-.f64 #s(literal 1/2 binary64) x)
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)) x)
(* -1 (sqrt (pow x 3)))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(* (pow x 2) (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x)))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (- 1 (* 2 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 3) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 2 binary64) (/.f64 #s(literal 1 binary64) x)) x)) (pow.f64 x #s(literal 3 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal -2 binary64) x) x x) x)
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x) x x) x)
1/8
#s(literal 1/8 binary64)
(+ 1/8 (* 1/16 (/ 1 x)))
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)) x)
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(* (pow x 2) (+ (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x))
(* -1 (* (pow x 3) (- (* 2 (/ 1 x)) 1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 2) x)) 1)))
(*.f64 (pow.f64 (neg.f64 x) #s(literal 3 binary64)) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (neg.f64 x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(*.f64 (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x) x x) x)

rewrite199.0ms (4.8%)

Memory

-16.3MiB live, 174.0MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	128
0	44	123
1	175	123
2	1083	123
0	8959	123

Stop Event

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

Counts

11 → 193

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(-.f64 x #s(literal 1/2 binary64))
(fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) x)) (/.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) x))) (.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)))) (+.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/512 binary64) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) (fma.f64 (/.f64 #s(literal -1/512 binary64) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) (/.f64 #s(literal -1/512 binary64) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) (*.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) (/.f64 #s(literal -1/512 binary64) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)))) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) #s(literal -1/512 binary64)))) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) #s(literal -1/512 binary64)))) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)))
(/.f64 (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) #s(literal 1/64 binary64))) (*.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))))
(/.f64 (-.f64 (.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) (.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)) #s(literal -1/512 binary64))) (*.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64))) (+.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) #s(literal -1/512 binary64))) (neg.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (neg.f64 (+.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) #s(literal -1/512 binary64)) (neg.f64 (neg.f64 (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) #s(literal -1/512 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x)))
(neg.f64 (neg.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))) (/.f64 #s(literal -1/64 binary64) (+.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 3 binary64)) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))) (/.f64 #s(literal -1/512 binary64) (+.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal 2 binary64)) #s(literal 1/64 binary64)) (/.f64 #s(literal -1/128 binary64) x))))
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))

eval39.0ms (0.9%)

Memory: 13.3MiB live, 57.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 9 092 to 1 114 computations (87.7% saved)

prune4.0ms (0.1%)

Memory

15.6MiB live, 15.6MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	236	3	239
Fresh	0	0	0
Picked	2	1	3
Done	0	2	2
Total	238	6	244

Accuracy

100.0%

Counts

244 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	57.1%	(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
▶	99.2%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
▶	99.4%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 80 to 63 computations (21.3% saved)

simplify16.0ms (0.4%)

Memory

-23.7MiB live, 20.7MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
cost-diff	0	#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
cost-diff	0	(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64))))
cost-diff	0	(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) x)
cost-diff	0	(/.f64 #s(literal -1/8 binary64) x)
cost-diff	0	(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
cost-diff	0	(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
cost-diff	0	(+.f64 x #s(literal -1/2 binary64))
cost-diff	0	(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
cost-diff	0	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	152
0	45	152
1	62	152
2	84	152
3	126	152
4	192	152
5	260	152
6	328	152
7	386	152
8	414	152
9	416	152
0	416	152

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(+.f64 x #s(literal -1/2 binary64))
x
#s(literal -1/2 binary64)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
#s(literal -1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
x
(-.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64))))
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(-.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(literal 1 binary64)
(/.f64 x (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 #s(literal -1/2 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(-.f64 (+.f64 #s(literal -1/2 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(+.f64 x #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) x)
x
#s(literal -1/2 binary64)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64))
(/.f64 #s(literal 1/16 binary64) x)
#s(literal 1/16 binary64)
#s(literal -1/8 binary64)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) x) #s(literal 1/2 binary64)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) x) #s(literal 1/2 binary64))
(/.f64 #s(literal -1/8 binary64) x)
#s(literal -1/8 binary64)
x
(-.f64 #s(literal 1/2 binary64) x)
#s(literal 1/2 binary64)
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
(sqrt.f64 (*.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64))))
(*.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(-.f64 x #s(literal 2 binary64))
x
#s(literal 2 binary64)
#s(literal 1 binary64)
(/.f64 x (-.f64 x #s(literal 1 binary64)))
(-.f64 x #s(literal 1 binary64))

localize96.0ms (2.3%)

Memory

-6.5MiB live, 98.6MiB allocated; 11ms collecting garbage

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x #s(literal 1 binary64))
accuracy	0.0	#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
accuracy	0.02734375	(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64))))
accuracy	27.458009355840794	(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
accuracy	0.0	(/.f64 #s(literal -1/8 binary64) x)
accuracy	0.0	(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
accuracy	0.0	(-.f64 #s(literal 1/2 binary64) x)
accuracy	0.5006805921162611	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
accuracy	0.0	(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
accuracy	0.0	(+.f64 x #s(literal -1/2 binary64))
accuracy	0.0390625	(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
accuracy	0.3807888781465246	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))

Samples

81.0ms

256×

valid

Compiler

Compiled 114 to 29 computations (74.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-mult: 40.0ms (57.8% of total)

ival-div: 10.0ms (14.5% of total)

ival-sub: 8.0ms (11.6% of total)

ival-sqrt: 5.0ms (7.2% of total)

ival-add: 3.0ms (4.3% of total)

ival-pow2: 3.0ms (4.3% of total)

exact: 1.0ms (1.4% of total)

adjust: 0.0ms (0% of total)

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

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

series5.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated; 0ms collecting garbage

Counts

13 → 53

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(+.f64 x #s(literal -1/2 binary64))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
(-.f64 #s(literal 1/2 binary64) x)
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64))))
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))

Outputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
-1/2
(- x 1/2)
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
1/2
(+ 1/2 (* -1 x))
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(* -1 x)
(* x (- x 1))
1
(+ 1 (* -2 x))
(+ 1 (* x (- x 2)))
-1
(- x 1)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(* x (- (* 1/2 (/ 1 x)) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(* x (- 1 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(* -1 (* x (- (/ 1 x) 1)))

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

((* (sqrt (- x 1)) (sqrt x)) (- (+ x -1/2) (/ (- (/ 1/16 x) -1/8) x)) (+ x -1/2) (/ (- (/ 1/16 x) -1/8) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) (- 1/2 x)) (/ -1/8 x) (- 1/2 x) (sqrt (* (pow (- 1 x) 2) (/ x (- x 1)))) (* (pow (- 1 x) 2) (/ x (- x 1))) (pow (- 1 x) 2) (+ (* (- x 2) x) 1) (- x 1))

1.0ms

inf

((* (sqrt (- x 1)) (sqrt x)) (- (+ x -1/2) (/ (- (/ 1/16 x) -1/8) x)) (+ x -1/2) (/ (- (/ 1/16 x) -1/8) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) (- 1/2 x)) (/ -1/8 x) (- 1/2 x) (sqrt (* (pow (- 1 x) 2) (/ x (- x 1)))) (* (pow (- 1 x) 2) (/ x (- x 1))) (pow (- 1 x) 2) (+ (* (- x 2) x) 1) (- x 1))

1.0ms

-inf

((* (sqrt (- x 1)) (sqrt x)) (- (+ x -1/2) (/ (- (/ 1/16 x) -1/8) x)) (+ x -1/2) (/ (- (/ 1/16 x) -1/8) x) (* (sqrt (- x 1)) (sqrt x)) (- (/ -1/8 x) (- 1/2 x)) (/ -1/8 x) (- 1/2 x) (sqrt (* (pow (- 1 x) 2) (/ x (- x 1)))) (* (pow (- 1 x) 2) (/ x (- x 1))) (pow (- 1 x) 2) (+ (* (- x 2) x) 1) (- x 1))

simplify101.0ms (2.4%)

Memory

13.7MiB live, 101.5MiB allocated; 15ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	187	540
1	589	487
2	2334	419
0	8240	406

Stop Event

1×	iter limit
1×	node limit

Counts

53 → 52

Calls

Call 1

Inputs
(* (sqrt x) (sqrt -1))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(/ -1/16 (pow x 2))
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
-1/2
(- x 1/2)
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/ -1/8 x)
(/ (- (* -1/2 x) 1/8) x)
(/ (- (* x (- x 1/2)) 1/8) x)
1/2
(+ 1/2 (* -1 x))
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(* -1 x)
(* x (- x 1))
1
(+ 1 (* -2 x))
(+ 1 (* x (- x 2)))
-1
(- x 1)
x
(* x (- 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(/ 1/8 x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(* x (- (* 1/2 (/ 1 x)) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(pow x 2)
(* (pow x 2) (- 1 (/ 1 x)))
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(* x (- 1 (/ 1 x)))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(* -1 (* x (- (/ 1 x) 1)))

Outputs
(* (sqrt x) (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x))
(+ (* 1/2 (* (sqrt (pow x 3)) (/ 1 (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt x) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 x) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* (sqrt x) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 5)))))))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))))) (.f64 x x))) (.f64 x x) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(/ -1/16 (pow x 2))
(/.f64 (/.f64 #s(literal -1/16 binary64) x) x)
(/ (- (* -1/8 x) 1/16) (pow x 2))
(/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(/ (- (* x (- (* -1/2 x) 1/8)) 1/16) (pow x 2))
(-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(/ (- (* x (- (* x (- x 1/2)) 1/8)) 1/16) (pow x 2))
(-.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)) (/.f64 #s(literal 1/16 binary64) (*.f64 x x)))
-1/2
#s(literal -1/2 binary64)
(- x 1/2)
(-.f64 x #s(literal 1/2 binary64))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* 1/8 x)) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* -1/2 x) 1/8) x)
(-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64))
(/ (- (* x (- x 1/2)) 1/8) x)
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 x))
(-.f64 #s(literal 1/2 binary64) x)
(+ (* -1 (* (sqrt (pow x 3)) (sqrt -1))) (* (sqrt x) (sqrt -1)))
(*.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64)))) (sqrt.f64 #s(literal -1 binary64)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* -1/2 (* (sqrt x) (/ 1 (sqrt -1)))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (.f64 (sqrt.f64 x) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) x (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)))
(+ (* x (+ (* -1 (* (sqrt x) (sqrt -1))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))))) (* (sqrt x) (sqrt -1)))
(fma.f64 (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 x)) (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x x)))
(* -1 x)
(neg.f64 x)
(* x (- x 1))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (* -2 x))
(fma.f64 #s(literal -2 binary64) x #s(literal 1 binary64))
(+ 1 (* x (- x 2)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
x
(* x (- 1 (* 1/2 (/ 1 x))))
(-.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x))))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* x (- (+ 1 (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) (pow x 2)))) (* 1/2 (/ 1 x))))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (+ 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
(* x (- (* 1/2 (/ 1 x)) 1))
(-.f64 #s(literal 1/2 binary64) x)
(* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* x (- (+ (/ 1/8 (pow x 2)) (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) 1))
(-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)) x)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (/ 1 x)))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x) x)
(* (pow x 2) (- 1 (* 2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 #s(literal -2 binary64) x) x x) x)
(* (pow x 2) (- (+ 1 (/ 1 (pow x 2))) (* 2 (/ 1 x))))
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x) x x) x)
(* x (- 1 (/ 1 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)) x)
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (+ (* -1/2 (/ (pow (sqrt -1) 2) x)) (pow (sqrt -1) 2))))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (+ (* -1 (/ (+ (* 1/8 (/ (pow (sqrt -1) 2) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* -1 (* x (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/8 (pow (sqrt -1) 2)) (* -1/16 (/ (pow (sqrt -1) 2) x))) x)) (* 1/2 (pow (sqrt -1) 2))) x)) (pow (sqrt -1) 2))))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1)))
(-.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x))) 1)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(* -1 (* x (- (* -1 (/ (- (* -1 (/ (+ 1/8 (* 1/16 (/ 1 x))) x)) 1/2) x)) 1)))
(-.f64 x (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)))
(* -1 (* x (- 1 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 1/2 binary64) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (* 1/8 (/ 1 x))) x)))))
(-.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* -1 (* x (+ 1 (* -1 (/ (+ 1/2 (+ (/ 1/16 (pow x 2)) (* 1/8 (/ 1 x)))) x)))))
(-.f64 (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal -1/2 binary64)) x)
(* (pow x 2) (+ 1 (* -1 (/ (- 2 (/ 1 x)) x))))
(*.f64 (fma.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64)) x) x x) x)
(* -1 (* x (- (/ 1 x) 1)))
(*.f64 (neg.f64 x) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))

rewrite288.0ms (7%)

Memory

-13.8MiB live, 273.5MiB allocated; 58ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	126
0	45	124
1	190	124
2	1362	124
0	8601	124

Stop Event

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

Counts

13 → 286

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
(-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))
(+.f64 x #s(literal -1/2 binary64))
(/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
(-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x))
(/.f64 #s(literal -1/8 binary64) x)
(-.f64 #s(literal 1/2 binary64) x)
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64))))
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(-.f64 x #s(literal 1 binary64))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 #s(literal -1/2 binary64) x) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
(/.f64 (+.f64 (pow.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 3 binary64))) (fma.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) x)) (-.f64 (+.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) x)) (-.f64 (pow.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 2 binary64)) (*.f64 (-.f64 (+.f64 #s(literal -1/2 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) x)) (/.f64 #s(literal -1/8 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 2 binary64)) (-.f64 (.f64 x x) (.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x))))
(/.f64 (+.f64 #s(literal -1/8 binary64) (pow.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 3 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))) (.f64 #s(literal -1/2 binary64) (-.f64 x (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (pow.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (pow.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 2 binary64)) (*.f64 x (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (+.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) (pow.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (+.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) (+.f64 #s(literal -1/2 binary64) x)))))
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(pow.f64 (.f64 (.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))) (*.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))) (neg.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (*.f64 (neg.f64 x) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) (sqrt.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (neg.f64 x))) (sqrt.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))) (sqrt.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (*.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))))
(exp.f64 (.f64 (log.f64 (.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) #s(literal 1/2 binary64))) (sinh.f64 (.f64 (log.f64 (.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) #s(literal 1/2 binary64))))
(.f64 (/.f64 (.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x) (-.f64 (*.f64 x x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x) (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(*.f64 (/.f64 x (-.f64 x #s(literal 1 binary64))) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))
(*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))))) (neg.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (neg.f64 x))) (neg.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x))) (neg.f64 (neg.f64 (-.f64 x #s(literal 1 binary64)))))
(/.f64 (*.f64 (neg.f64 x) #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (neg.f64 x)) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x) (-.f64 x #s(literal 1 binary64)))
#s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x))) (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x))) (-.f64 (.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) #s(literal -1 binary64)) (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) #s(literal -1 binary64))) (.f64 (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x))) (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 2 binary64)) x))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64))) (.f64 (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (fma.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) #s(literal 1 binary64))) (.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64))) (-.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x))))
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x))))
(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x)))
(fma.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64))
(fma.f64 x (*.f64 (-.f64 x #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(fma.f64 x (-.f64 x #s(literal 2 binary64)) #s(literal 1 binary64))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 (-.f64 x #s(literal 2 binary64)) x))) (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 2 binary64)) x))))
(-.f64 (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64))) (pow.f64 (-.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (-.f64 x #s(literal 2 binary64))) x))
(-.f64 #s(literal 1 binary64) (*.f64 (neg.f64 x) (-.f64 x #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)))) (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x)))))
(+.f64 (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x)) #s(literal -1 binary64)) (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x))))
(+.f64 (/.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (.f64 (-.f64 x #s(literal 2 binary64)) x))) (pow.f64 (-.f64 (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (-.f64 x #s(literal 2 binary64)) x)) #s(literal -1 binary64)))
(+.f64 (*.f64 (-.f64 x #s(literal 2 binary64)) x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 x #s(literal 2 binary64)) x))
(*.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))) (*.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) (neg.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)))
(-.f64 x #s(literal 1 binary64))

eval47.0ms (1.1%)

Memory: 36.6MiB live, 81.6MiB allocated; 4ms collecting garbage
Compiler: Compiled 11 604 to 1 561 computations (86.5% saved)

prune11.0ms (0.3%)

Memory

-18.1MiB live, 25.8MiB allocated; 6ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	326	1	327
Fresh	0	0	0
Picked	2	1	3
Done	0	3	3
Total	328	5	333

Accuracy

100.0%

Counts

333 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	57.1%	(sqrt.f64 #s(approx (* (pow (- 1 x) 2) (/ x (- x 1))) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
✓	99.2%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
✓	98.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.5%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 247 to 107 computations (56.7% saved)

regimes7.0ms (0.2%)

Memory

15.6MiB live, 15.6MiB allocated; 0ms collecting garbage

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(sqrt.f64 #s(approx (* (pow (- 1 x) 2) (/ x (- x 1))) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) #s(literal 1 binary64) x))
(sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) (/.f64 x (-.f64 x #s(literal 1 binary64)))))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)) x) x x))
(/.f64 (sqrt.f64 (*.f64 #s(approx (pow (- 1 x) 2) (fma.f64 (-.f64 x #s(literal 2 binary64)) x #s(literal 1 binary64))) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) x)) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))

Calls

2 calls:

3.0ms	x
3.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

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

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes8.0ms (0.2%)

Memory

-48.3MiB live, 8.7MiB allocated; 6ms collecting garbage

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(sqrt.f64 #s(approx (* (pow (- 1 x) 2) (/ x (- x 1))) (*.f64 (-.f64 x #s(literal 1 binary64)) x)))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))

Calls

2 calls:

5.0ms	(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
2.0ms	x

Results

Accuracy	Segments	Branch
99.2%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
99.2%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

5.8MiB live, 5.8MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
98.9%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.9%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0.1%)

Memory

5.0MiB live, 5.0MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
97.5%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
97.5%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify57.0ms (1.4%)

Memory

11.3MiB live, 58.1MiB allocated; 2ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	54
1	36	54
2	57	54
3	75	54
4	107	54
5	152	54
6	204	54
7	249	54
8	294	54
9	313	54
10	495	54
11	3406	54

Stop Event

1×	node limit

Calls

Call 1

Inputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (+.f64 x #s(literal -1/2 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) (-.f64 #s(literal 1/2 binary64) x)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

derivations685.0ms (16.6%)

Memory

-2.7MiB live, 369.2MiB allocated; 33ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	202	655
1	658	591
2	2630	512
0	8834	497
0	150	457
1	495	390
2	2202	378
3	7444	375
0	8362	345
0	28	132
0	45	128
1	166	125
2	1012	116
0	9308	114
0	29	128
0	44	123
1	175	123
2	1083	123
0	8959	123

Stop Event

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

Compiler

Compiled 54 to 23 computations (57.4% saved)

preprocess22.0ms (0.5%)

Memory: 24.5MiB live, 24.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 122 to 58 computations (52.5% saved)

end0.0ms (0%)

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

Iter	Nodes	Cost
0	30	152
0	45	152
1	62	152
2	84	152
3	126	152
4	192	152
5	260	152
6	328	152
7	386	152
8	414	152
9	416	152
0	416	152

Iter	Nodes	Cost
0	30	152
0	45	152
1	62	152
2	84	152
3	126	152
4	192	152
5	260	152
6	328	152
7	386	152
8	414	152
9	416	152
0	416	152

start0.0ms (0%)

analyze1.0ms (0%)

sample926.0ms (22.4%)

explain73.0ms (1.8%)

preprocess17.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize17.0ms (0.4%)

series8.0ms (0.2%)

simplify138.0ms (3.3%)

rewrite223.0ms (5.4%)

eval67.0ms (1.6%)

prune6.0ms (0.1%)

simplify91.0ms (2.2%)

localize64.0ms (1.5%)

series56.0ms (1.4%)

simplify183.0ms (4.4%)

rewrite251.0ms (6.1%)

eval65.0ms (1.6%)

prune7.0ms (0.2%)

simplify77.0ms (1.9%)

localize96.0ms (2.3%)

series3.0ms (0.1%)

simplify175.0ms (4.2%)

rewrite199.0ms (4.8%)

eval39.0ms (0.9%)

prune4.0ms (0.1%)

simplify16.0ms (0.4%)

localize96.0ms (2.3%)

series5.0ms (0.1%)

simplify101.0ms (2.4%)

rewrite288.0ms (7%)

eval47.0ms (1.1%)

prune11.0ms (0.3%)

regimes7.0ms (0.2%)

regimes8.0ms (0.2%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

simplify57.0ms (1.4%)

derivations685.0ms (16.6%)

preprocess22.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	30	152
0	45	152
1	62	152
2	84	152
3	126	152
4	192	152
5	260	152
6	328	152
7	386	152
8	414	152
9	416	152
0	416	152