Metrics for sqrt times

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze2.0ms (0%)

Memory

2.8MiB live, 2.8MiB allocated

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)

sample1.0s (31%)

Memory

40.4MiB live, 850.6MiB allocated

Samples

746.0ms	8 247×	0	valid
1.0ms	9×	1	valid
0.0ms	8×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 312.0ms

ival-sqrt: 129.0ms (41.3% of total)

ival-mult: 111.0ms (35.6% of total)

ival-sub: 57.0ms (18.3% of total)

ival-true: 6.0ms (1.9% of total)

exact: 5.0ms (1.6% of total)

ival-assert: 4.0ms (1.3% of total)

adjust: 0.0ms (0% of total)

Bogosity

explain59.0ms (1.8%)

Memory

18.8MiB live, 113.2MiB allocated

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

25.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-sqrt: 7.0ms (52.2% of total)

ival-sub: 3.0ms (22.4% of total)

ival-mult: 3.0ms (22.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess13.0ms (0.4%)

Memory

19.1MiB live, 19.1MiB allocated

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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

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)

simplify4.0ms (0.1%)

Memory

4.4MiB live, 4.4MiB allocated

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)

localize22.0ms (0.7%)

Memory

-27.4MiB live, 26.4MiB allocated

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

Samples

17.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-sqrt: 7.0ms (61.9% of total)

ival-mult: 2.0ms (17.7% of total)

ival-sub: 1.0ms (8.8% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.2%)

Memory

4.3MiB live, 4.3MiB allocated

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
2.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))
1.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (sqrt (- x 1)) (- x 1) (sqrt x))

simplify155.0ms (4.6%)

Memory

18.5MiB live, 106.1MiB allocated

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)))

rewrite189.0ms (5.6%)

Memory

-4.6MiB live, 180.1MiB allocated

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))))
(.f64 (.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 (pow.f64 x #s(literal 1/4 binary64)) (neg.f64 (pow.f64 (-.f64 x #s(literal 1 binary64)) #s(literal 1/4 binary64)))))
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(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))))

eval68.0ms (2%)

Memory: -28.9MiB live, 117.7MiB allocated
Compiler: Compiled 7 786 to 1 459 computations (81.3% saved)

prune5.0ms (0.2%)

Memory

24.7MiB live, 24.7MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	375	3	378
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	375	4	379

Accuracy

100.0%

Counts

379 → 4

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))
▶	92.4%	(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
▶	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
▶	97.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 37 to 29 computations (21.6% saved)

simplify215.0ms (6.4%)

Memory

-1.5MiB live, 289.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f64 x)
cost-diff	0	(expm1.f64 (log.f64 x))
cost-diff	0	(sqrt.f64 (expm1.f64 (log.f64 x)))
cost-diff	0	(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 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: 2 (0.0ms)

Iter	Nodes	Cost
0	16	54
0	25	54
1	38	54
2	84	48
3	267	48
4	869	48
5	6771	48
0	8406	48

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
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(expm1.f64 (log.f64 x))
(log.f64 x)
x
(sqrt.f64 x)

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
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(*.f64 (sqrt.f64 x) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(sqrt.f64 (-.f64 x #s(literal 1 binary64)))
(expm1.f64 (log.f64 x))
(-.f64 x #s(literal 1 binary64))
(log.f64 x)
x
(sqrt.f64 x)

localize58.0ms (1.7%)

Memory

-27.8MiB live, 32.6MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 x)
accuracy	0.0	(log.f64 x)
accuracy	0.5	(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
accuracy	5.775663634849974	(expm1.f64 (log.f64 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	1.0903332399866426	#s(approx (* (sqrt (- x 1)) (sqrt x)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
accuracy	1.3217135623575784	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Samples

49.0ms

256×

valid

Compiler

Compiled 54 to 16 computations (70.4% saved)

Precisions

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

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

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

ival-expm1: 3.0ms (14.9% of total)

ival-log: 3.0ms (14.9% of total)

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

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

ival-add: 1.0ms (5% of total)

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

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

exact: 0.0ms (0% of total)

series61.0ms (1.8%)

Memory

33.0MiB live, 77.3MiB allocated

Counts

9 → 35

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)
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(expm1.f64 (log.f64 x))
(log.f64 x)
(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)))))))))
-1/2
(- x 1/2)
(/ -1/2 x)
(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)
(log x)
(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 (log (/ 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 (* (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)))
(+ (log -1) (* -1 (log (/ -1 x))))

Calls

3 calls:

Time	Variable		Point	Expression
23.0ms	x	@	0	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (* (sqrt (- (exp (log x)) 1)) (sqrt x)) (sqrt (- (exp (log x)) 1)) (- (exp (log x)) 1) (log x) (sqrt x))
20.0ms	x	@	inf	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (* (sqrt (- (exp (log x)) 1)) (sqrt x)) (sqrt (- (exp (log x)) 1)) (- (exp (log x)) 1) (log x) (sqrt x))
17.0ms	x	@	-inf	((* (sqrt (- x 1)) (sqrt x)) (+ (* (/ -1/2 x) x) x) (* (sqrt (- x 1)) (sqrt x)) (/ -1/2 x) (* (sqrt (- (exp (log x)) 1)) (sqrt x)) (sqrt (- (exp (log x)) 1)) (- (exp (log x)) 1) (log x) (sqrt x))

Time

Variable

Point

Expression

23.0ms

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

20.0ms

inf

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

17.0ms

-inf

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

simplify179.0ms (5.3%)

Memory

-27.4MiB live, 111.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	163	483
1	520	415
2	2248	403
3	7555	400
0	8087	369

Stop Event

1×	iter limit
1×	node limit

Counts

35 → 34

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

rewrite151.0ms (4.5%)

Memory

42.3MiB live, 275.0MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	50
0	25	47
1	73	47
2	401	41
3	5549	41
0	8076	41

Stop Event

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

Counts

9 → 279

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)
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))
(sqrt.f64 (expm1.f64 (log.f64 x)))
(expm1.f64 (log.f64 x))
(log.f64 x)
(sqrt.f64 x)

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) x)
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1/4 binary64)) (-.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x #s(literal 1/2 binary64)) #s(literal 1/4 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (-.f64 #s(literal 1/16 binary64) (pow.f64 (.f64 (-.f64 x #s(literal -1/2 binary64)) x) #s(literal 2 binary64)))) (-.f64 #s(literal 1/4 binary64) (*.f64 (-.f64 x #s(literal -1/2 binary64)) x)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (pow.f64 (.f64 (-.f64 x #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1/64 binary64))) (fma.f64 (.f64 (-.f64 x #s(literal -1/2 binary64)) x) (-.f64 (.f64 (-.f64 x #s(literal -1/2 binary64)) x) #s(literal 1/4 binary64)) #s(literal 1/16 binary64)))
(*.f64 (/.f64 (fma.f64 (neg.f64 x) x #s(literal 1/4 binary64)) (fma.f64 (neg.f64 x) x #s(literal 1/4 binary64))) (-.f64 x #s(literal 1/2 binary64)))
(.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 (fma.f64 (-.f64 x #s(literal -1/2 binary64)) x #s(literal 1/4 binary64)) (/.f64 (-.f64 x #s(literal 1/2 binary64)) (fma.f64 (-.f64 x #s(literal -1/2 binary64)) x #s(literal 1/4 binary64))))
(*.f64 (-.f64 x #s(literal 1/2 binary64)) (/.f64 (-.f64 #s(literal -1/2 binary64) x) (-.f64 #s(literal -1/2 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 (-.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 3 binary64)) #s(literal 1 binary64)) x) (-.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 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64))) (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (*.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x)))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) (+.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64)))) (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (*.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x)))))
(/.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 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64))) (pow.f64 x #s(literal -1 binary64)))
(/.f64 (*.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal -1 binary64)))
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(*.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) x)))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))) (fma.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 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -2 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 (-.f64 (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 2 binary64)) (pow.f64 (-.f64 (sinh.f64 (log.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64))) (-.f64 (cosh.f64 (log.f64 x)) (-.f64 (sinh.f64 (log.f64 x)) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 x (/.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 3 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 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -2 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 (+.f64 (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (-.f64 (sinh.f64 (log.f64 x)) #s(literal 1 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (-.f64 (sinh.f64 (log.f64 x)) #s(literal 1 binary64)) #s(literal 2 binary64)) (*.f64 (cosh.f64 (log.f64 x)) (-.f64 (sinh.f64 (log.f64 x)) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64)))) (neg.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(/.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 (fma.f64 x x (pow.f64 x #s(literal 3 binary64))) (+.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))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #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)) #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 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #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)) #s(literal 1 binary64)) (*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64)))
(/.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 (fma.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 x #s(literal 1 binary64)) #s(literal 1 binary64))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x x #s(literal -1 binary64))) (+.f64 #s(literal 1 binary64) x)))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(neg.f64 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 #s(literal -1 binary64) x #s(literal -1 binary64))))
(neg.f64 (/.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)))))
(expm1.f64 (*.f64 (log.f64 x) #s(literal 1 binary64)))
(expm1.f64 (log.f64 x))
(-.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 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))
(+.f64 (-.f64 (sinh.f64 (log.f64 x)) #s(literal 1 binary64)) (cosh.f64 (log.f64 x)))
(+.f64 (sinh.f64 (log.f64 x)) (-.f64 (cosh.f64 (log.f64 x)) #s(literal 1 binary64)))
(+.f64 (cosh.f64 (log.f64 x)) (-.f64 (sinh.f64 (log.f64 x)) #s(literal 1 binary64)))
(neg.f64 (neg.f64 (log.f64 x)))
(-.f64 (log.f64 (-.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 2 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 2 binary64)))) (log.f64 (-.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x)))))
(-.f64 (log.f64 (fma.f64 #s(literal 2 binary64) (sinh.f64 (log.f64 x)) (+.f64 (pow.f64 x #s(literal -1 binary64)) x))) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 (fma.f64 #s(literal 2 binary64) (cosh.f64 (log.f64 x)) (-.f64 x (pow.f64 x #s(literal -1 binary64))))) (log.f64 #s(literal 2 binary64)))
(-.f64 (log.f64 (neg.f64 (+.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64))))) (log.f64 (neg.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x)))))))
(-.f64 (log.f64 (.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64))))) (log.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (*.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x))))))
(-.f64 (log.f64 (.f64 (+.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64))) #s(literal 1 binary64))) (log.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (*.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x))))))
(-.f64 (log.f64 (fma.f64 (-.f64 x (pow.f64 x #s(literal -1 binary64))) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (+.f64 (pow.f64 x #s(literal -1 binary64)) x)))) (log.f64 #s(literal 4 binary64)))
(-.f64 (log.f64 (fma.f64 (+.f64 (pow.f64 x #s(literal -1 binary64)) x) #s(literal 2 binary64) (*.f64 #s(literal 2 binary64) (-.f64 x (pow.f64 x #s(literal -1 binary64)))))) (log.f64 #s(literal 4 binary64)))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (pow.f64 x #s(literal -1 binary64)))))
(-.f64 (log.f64 (+.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64)))) (log.f64 (+.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 2 binary64)) (-.f64 (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 2 binary64)) (*.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x)))))))
(-.f64 (log.f64 (+.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64)))) (log.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x))))))
(-.f64 #s(literal 0 binary64) (neg.f64 (log.f64 x)))
(+.f64 #s(literal 0 binary64) (log.f64 x))
(+.f64 (log.f64 x) #s(literal 0 binary64))
(log.f64 x)
(*.f64 (pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (neg.f64 (fabs.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fabs.f64 (fabs.f64 x)) #s(literal 1/4 binary64)) (pow.f64 (fabs.f64 (fabs.f64 x)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (fabs.f64 x) #s(literal 1/4 binary64)) (pow.f64 (fabs.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 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) (fabs.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 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (pow.f64 x #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (fabs.f64 x) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1/2 binary64))
(/.f64 (hypot.f64 (pow.f64 (sinh.f64 (log.f64 x)) #s(literal 3/2 binary64)) (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3/2 binary64))) (sqrt.f64 (-.f64 (cosh.f64 (.f64 #s(literal 2 binary64) (log.f64 x))) (.f64 (sinh.f64 (log.f64 x)) (cosh.f64 (log.f64 x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 x #s(literal -1 binary64))))
(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 (log.f64 (pow.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 x) #s(literal 2 binary64)))
(exp.f64 (log.f64 (sqrt.f64 x)))
(+.f64 (cosh.f64 (/.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (/.f64 (log.f64 x) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (log.f64 (sqrt.f64 x))) (sinh.f64 (log.f64 (sqrt.f64 x))))

eval62.0ms (1.8%)

Memory: 5.9MiB live, 49.8MiB allocated
Compiler: Compiled 6 583 to 1 211 computations (81.6% saved)

prune18.0ms (0.5%)

Memory

-30.0MiB live, 15.3MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	0	0	0
Picked	2	1	3
Done	1	0	1
Total	309	3	312

Accuracy

100.0%

Counts

312 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	57.5%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
▶	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 26 to 21 computations (19.2% saved)

simplify3.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 5 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f64 x #s(literal 1 binary64))
cost-diff	0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
cost-diff	0	(sqrt.f64 (*.f64 (-.f64 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	12	32
0	16	32
1	20	32
0	20	32

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

localize24.0ms (0.7%)

Memory

31.4MiB live, 31.4MiB allocated

Localize:

Found 5 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 x #s(literal 1 binary64))
accuracy	0.0	(*.f64 (-.f64 x #s(literal 1 binary64)) x)
accuracy	27.17858828303527	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
accuracy	0.0	(-.f64 x #s(literal 1/2 binary64))
accuracy	1.0903332399866426	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))

Samples

17.0ms

256×

valid

Compiler

Compiled 30 to 12 computations (60% saved)

Precisions

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

ival-sqrt: 5.0ms (46.8% of total)

ival-sub: 3.0ms (28.1% of total)

ival-mult: 3.0ms (28.1% of total)

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

exact: 0.0ms (0% of total)

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

series67.0ms (2%)

Memory

-16.6MiB live, 44.3MiB allocated

Counts

5 → 26

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

Calls

3 calls:

Time

Variable

Point

Expression

44.0ms

inf

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

22.0ms

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

1.0ms

-inf

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

simplify229.0ms (6.8%)

Memory

-5.6MiB live, 182.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	275
1	358	251
2	1512	244
3	6420	241
0	8559	228

Stop Event

1×	iter limit
1×	node limit

Counts

26 → 25

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 x)
(* x (- x 1))
-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))))
(pow x 2)
(* (pow x 2) (- 1 (/ 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 (* 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)))))
(* -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 (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))) (.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 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (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 (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 x)
(neg.f64 x)
(* x (- x 1))
(*.f64 (-.f64 x #s(literal 1 binary64)) x)
-1
#s(literal -1 binary64)
(- x 1)
(-.f64 x #s(literal 1 binary64))
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)
(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)
(* 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 (* x (- (* 1/2 (/ 1 x)) 1)))
(fma.f64 (/.f64 #s(literal -1/2 binary64) x) 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)
(* -1 (* x (- (/ 1 x) 1)))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) (neg.f64 x))

rewrite186.0ms (5.5%)

Memory

-23.0MiB live, 167.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
0	16	27
1	49	27
2	234	27
3	1918	27
0	8549	27

Stop Event

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

Counts

5 → 346

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

Outputs
#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
(.f64 (/.f64 (-.f64 (.f64 x x) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x x (-.f64 #s(literal 1/4 binary64) (*.f64 #s(literal 1/2 binary64) x))))
(.f64 (/.f64 (-.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (*.f64 x x) #s(literal 1/4 binary64))) (-.f64 x #s(literal 1/2 binary64)))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (+.f64 (pow.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) (-.f64 (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)) (.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)))) (neg.f64 (/.f64 (fma.f64 x x #s(literal 1/4 binary64)) (+.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64)))) (neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64))))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))))) (neg.f64 (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) x)) (*.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal 1/4 binary64)))) (neg.f64 (pow.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) (.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal 1/8 binary64)))) (neg.f64 (pow.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal 2 binary64))))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64))) (*.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64)) #s(literal -1/4 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (neg.f64 (.f64 x x)) (+.f64 #s(literal 1/2 binary64) x)) (.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64)) #s(literal 1/4 binary64))) (.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64)) (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (.f64 (.f64 x x) (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal -1/4 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) x) (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))) (.f64 (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal -1/8 binary64))) (pow.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) (.f64 (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 1/8 binary64))) (*.f64 (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))) (.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal -1/8 binary64))) (*.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (neg.f64 (*.f64 x x)) #s(literal -1/4 binary64)) (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal -1/8 binary64)) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64))) (/.f64 (fma.f64 x x #s(literal 1/4 binary64)) (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64))) (/.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x)) #s(literal 2 binary64)) (.f64 (*.f64 x (/.f64 x (+.f64 #s(literal 1/2 binary64) x))) (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal 1/2 binary64) x))))))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) #s(literal 2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) (/.f64 #s(literal 1/8 binary64) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/512 binary64))) (neg.f64 (*.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/64 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64)))) (neg.f64 (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64))) (neg.f64 (*.f64 (fma.f64 x x #s(literal 1/4 binary64)) (+.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64))) (neg.f64 (.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/2 binary64) x))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64))) (neg.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) x)) (*.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1/2 binary64) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))) (.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/16 binary64)) (*.f64 (fma.f64 x x #s(literal 1/4 binary64)) (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64)) (.f64 (+.f64 (fma.f64 #s(literal 1/4 binary64) (.f64 x x) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1/2 binary64) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/64 binary64)) (*.f64 (+.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) #s(literal 1/512 binary64)) (*.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3 binary64)) #s(literal 1/64 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64))) (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (neg.f64 (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(/.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64)) (+.f64 #s(literal 1/2 binary64) x))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64))))
(neg.f64 (/.f64 (neg.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64))) (+.f64 #s(literal 1/2 binary64) x)))
(neg.f64 (/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (fma.f64 x x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 (-.f64 (*.f64 x x) #s(literal 1/4 binary64)) (fma.f64 #s(literal -1 binary64) x #s(literal -1/2 binary64))))
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(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 (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 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (+.f64 #s(literal 1 binary64) x)))) (/.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (+.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 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -2 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 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -2 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 (/.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 x x (+.f64 #s(literal 1 binary64) x))) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #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 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 x x (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (+.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 x x (+.f64 #s(literal 1 binary64) x)))) (/.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 x x (+.f64 #s(literal 1 binary64) x)))))
(-.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 x x (+.f64 #s(literal 1 binary64) x))) (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))))
(-.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 x x (+.f64 #s(literal 1 binary64) x))) (/.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 x x (+.f64 #s(literal 1 binary64) x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (/.f64 (pow.f64 (fma.f64 x x (+.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(literal 1 binary64)))
(-.f64 (/.f64 x #s(literal 1 binary64)) #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 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))
(exp.f64 (log.f64 (-.f64 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)))))

eval41.0ms (1.2%)

Memory: 25.6MiB live, 68.2MiB allocated
Compiler: Compiled 8 265 to 1 451 computations (82.4% saved)

prune8.0ms (0.3%)

Memory

-19.1MiB live, 25.7MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	368	0	368
Fresh	0	0	0
Picked	0	2	2
Done	0	1	1
Total	368	3	371

Accuracy

100.0%

Counts

371 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	57.5%	(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
✓	98.3%	#s(approx (* (sqrt (- x 1)) (sqrt x)) (-.f64 x #s(literal 1/2 binary64)))
✓	97.9%	#s(approx (* (sqrt (- x 1)) (sqrt x)) x)

Compiler

Compiled 80 to 46 computations (42.5% saved)

regimes5.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

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)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))
(sqrt.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x))
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(*.f64 (sqrt.f64 (expm1.f64 (log.f64 x))) (sqrt.f64 x))

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

Calls

2 calls:

2.0ms	(*.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)

regimes4.0ms (0.1%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

4 → 2

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
100.0%	2	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes3.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Counts

3 → 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)) (fma.f64 (/.f64 #s(literal -1/2 binary64) x) x x))

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
98.3%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
98.3%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

regimes2.0ms (0.1%)

Memory

6.8MiB live, 6.8MiB allocated

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
97.9%	1	`(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
97.9%	1	`x`

Compiler

Compiled 8 to 7 computations (12.5% saved)

bsearch5.0ms (0.1%)

Memory

-39.4MiB live, 5.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
3.0ms	1811482795888.6235	161893269376789950.0

Samples

1.0ms

32×

valid

Compiler

Compiled 40 to 38 computations (5% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

exact: 0.0ms (0% of total)

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

simplify10.0ms (0.3%)

Memory

24.4MiB live, 24.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	46
1	26	46
2	33	46
3	37	46
4	41	46
5	55	46

Stop Event

1×

saturated

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(if (<=.f64 x #s(literal 1000000000000000 binary64)) (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #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)) x)

Outputs
(*.f64 (sqrt.f64 (-.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(if (<=.f64 x #s(literal 1000000000000000 binary64)) (sqrt.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x)) #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)) x)

derivations419.0ms (12.4%)

Memory

5.8MiB live, 300.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	50
0	25	47
1	73	47
2	401	41
3	5549	41
0	8076	41
0	150	457
1	495	390
2	2202	378
3	7444	375
0	8362	345
0	6	16
0	10	15
1	32	15
2	148	15
3	1189	15
0	9614	13

Stop Event

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

Compiler

Compiled 46 to 20 computations (56.5% saved)

preprocess51.0ms (1.5%)

Memory: 0.5MiB live, 44.9MiB allocated
Compiler: Compiled 106 to 52 computations (50.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze2.0ms (0%)

sample1.0s (31%)

explain59.0ms (1.8%)

preprocess13.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize22.0ms (0.7%)

series5.0ms (0.2%)

simplify155.0ms (4.6%)

rewrite189.0ms (5.6%)

eval68.0ms (2%)

prune5.0ms (0.2%)

simplify215.0ms (6.4%)

localize58.0ms (1.7%)

series61.0ms (1.8%)

simplify179.0ms (5.3%)

rewrite151.0ms (4.5%)

eval62.0ms (1.8%)

prune18.0ms (0.5%)

simplify3.0ms (0.1%)

localize24.0ms (0.7%)

series67.0ms (2%)

simplify229.0ms (6.8%)

rewrite186.0ms (5.5%)

eval41.0ms (1.2%)

prune8.0ms (0.3%)

regimes5.0ms (0.1%)

regimes4.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0.1%)

bsearch5.0ms (0.1%)

simplify10.0ms (0.3%)

derivations419.0ms (12.4%)

preprocess51.0ms (1.5%)

end0.0ms (0%)

Profiling