Metrics for Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3

start0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze2.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample677.0ms (25.4%)

Memory

-12.4MiB live, 1 162.4MiB allocated; 178ms collecting garbage

Samples

462.0ms	8 256×	0	valid
0.0ms	3×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 291.0ms

ival-sqrt: 131.0ms (45% of total)

ival-mult: 103.0ms (35.4% of total)

ival-sub: 41.0ms (14.1% of total)

ival-true: 6.0ms (2.1% of total)

exact: 5.0ms (1.7% of total)

ival-assert: 3.0ms (1% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

explain174.0ms (6.5%)

Memory

46.0MiB live, 91.0MiB allocated; 5ms collecting garbage

FPErrors

Click to see full error table

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

22.0ms

512×

valid

Compiler

Compiled 42 to 19 computations (54.8% saved)

Precisions

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

ival-mult: 4.0ms (35.9% of total)

ival-sqrt: 4.0ms (35.9% of total)

ival-sub: 3.0ms (26.9% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess58.0ms (2.2%)

Memory

-44.8MiB live, 19.7MiB allocated; 86ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	21	13
2	45	13
3	56	13
4	71	13
0	5	6
0	8	6
1	16	6
2	37	6
3	63	6
4	78	6
0	78	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.2%)

Memory

4.3MiB live, 4.3MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	16	16
2	37	16
3	63	16
4	78	16
0	78	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize15.0ms (0.6%)

Memory

23.1MiB live, 23.1MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	0.0078125	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))

Samples

10.0ms

256×

valid

Compiler

Compiled 18 to 7 computations (61.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-mult: 2.0ms (37.5% of total)

ival-sqrt: 2.0ms (37.5% of total)

ival-sub: 1.0ms (18.7% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Counts

3 → 16

Calls

Call 1

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

Outputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

Calls

3 calls:

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

simplify147.0ms (5.5%)

Memory

-21.1MiB live, 166.0MiB allocated; 55ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	220
1	156	219
2	475	203
3	1620	192
4	5992	192
0	8180	181

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 16

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(+ 1 (* -1 (pow x 2)))
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

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

rewrite161.0ms (6.1%)

Memory

-8.6MiB live, 181.5MiB allocated; 34ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	11
1	38	11
2	241	11
3	2203	11
0	8263	10

Stop Event

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

Counts

3 → 226

Calls

Call 1

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

Outputs
(*.f64 (pow.f64 (sqrt.f64 (sin.f64 (acos.f64 x))) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (sin.f64 (acos.f64 x))) #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 (sqrt.f64 (sin.f64 (acos.f64 x))))) (neg.f64 (neg.f64 (sqrt.f64 (sin.f64 (acos.f64 x))))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))))) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (sin.f64 (acos.f64 x)))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64)))) (sqrt.f64 (fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sin.f64 (acos.f64 x)))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(*.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64)) #s(literal 1 binary64))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64))))
(*.f64 (neg.f64 (sqrt.f64 (sin.f64 (acos.f64 x)))) (neg.f64 (sqrt.f64 (sin.f64 (acos.f64 x)))))
(*.f64 (sqrt.f64 (sin.f64 (acos.f64 x))) (sqrt.f64 (sin.f64 (acos.f64 x))))
(*.f64 (sin.f64 (acos.f64 x)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sin.f64 (acos.f64 x)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 (*.f64 x x)))
(pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (neg.f64 (sqrt.f64 (sin.f64 (acos.f64 x)))) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (sin.f64 (acos.f64 x))) #s(literal 2 binary64))
(pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1/2 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x)))) (.f64 (.f64 #s(literal 0 binary64) x) (.f64 #s(literal 0 binary64) x))) (sin.f64 (acos.f64 x)))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 0 binary64) x) (.f64 #s(literal 0 binary64) x)) (.f64 (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))))) (-.f64 (.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x)))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 0 binary64)) (.f64 x #s(literal 0 binary64))) (.f64 (sin.f64 (acos.f64 x)) (sin.f64 (acos.f64 x)))) (-.f64 (*.f64 x #s(literal 0 binary64)) (sin.f64 (acos.f64 x))))
(/.f64 (-.f64 (.f64 (cosh.f64 (log.f64 (sin.f64 (acos.f64 x)))) (cosh.f64 (log.f64 (sin.f64 (acos.f64 x))))) (.f64 (sinh.f64 (log.f64 (sin.f64 (acos.f64 x)))) (sinh.f64 (log.f64 (sin.f64 (acos.f64 x)))))) (-.f64 (cosh.f64 (log.f64 (sin.f64 (acos.f64 x)))) (sinh.f64 (log.f64 (sin.f64 (acos.f64 x))))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 0 binary64) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) (fma.f64 (.f64 #s(literal 0 binary64) x) (.f64 #s(literal 0 binary64) x) (.f64 (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) (*.f64 #s(literal 0 binary64) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 0 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 0 binary64) x) (.f64 #s(literal 0 binary64) x) (-.f64 (.f64 (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x))) (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x)))) (.f64 (.f64 #s(literal 0 binary64) x) (.f64 #s(literal 1 binary64) (sin.f64 (acos.f64 x)))))))
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(-.f64 (/.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -3 binary64)) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))))))) (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64))) (+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))))))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -3 binary64)) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) #s(literal 2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))))) (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) #s(literal 2 binary64)) (.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64))) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 x x #s(literal 1 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 8 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (pow.f64 x #s(literal 18 binary64)) (.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))))
(-.f64 (/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 12 binary64))) (pow.f64 x #s(literal 6 binary64)))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(-.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(exp.f64 (log1p.f64 (*.f64 x x)))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 8 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))) (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))))))
(+.f64 (cosh.f64 (log1p.f64 (.f64 x x))) (sinh.f64 (log1p.f64 (.f64 x x))))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)))
(+.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))) (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
(+.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1 binary64) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(.f64 (fabs.f64 (.f64 #s(literal -1 binary64) x)) x)
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 x))
(.f64 (.f64 #s(literal -1 binary64) x) x)
(*.f64 (sqrt.f64 x) (sqrt.f64 (pow.f64 x #s(literal 3 binary64))))
(.f64 #s(literal -1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal -1 binary64))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))) (-.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64)))))))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval33.0ms (1.2%)

Memory: 18.2MiB live, 61.6MiB allocated; 7ms collecting garbage
Compiler: Compiled 5 253 to 846 computations (83.9% saved)

prune4.0ms (0.1%)

Memory

15.3MiB live, 15.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	238	4	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	238	5	243

Accuracy

100.0%

Counts

243 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
▶	100.0%	(sin.f64 (acos.f64 x))
▶	99.8%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
▶	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
▶	99.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 49 to 38 computations (22.4% saved)

simplify15.0ms (0.5%)

Memory

-30.9MiB live, 14.2MiB allocated; 9ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	90
0	27	90
1	46	90
2	116	90
3	250	90
4	399	90
5	429	90
6	429	90
0	429	90

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize59.0ms (2.2%)

Memory

44.9MiB live, 87.5MiB allocated; 8ms collecting garbage

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0	(sin.f64 (acos.f64 x))
accuracy	0.0	(acos.f64 x)
accuracy	0.0	(-.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(.f64 #s(literal -1/8 binary64) (.f64 x x))
accuracy	0.1495469356347079	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (-.f64 (.f64 #s(literal -1/8 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
accuracy	0.0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.25889541663693993	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
accuracy	0.6199836994360013	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Samples

49.0ms

256×

valid

Compiler

Compiled 72 to 18 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-sin: 22.0ms (57.4% of total)

ival-mult: 7.0ms (18.3% of total)

ival-add: 2.0ms (5.2% of total)

ival-acos: 2.0ms (5.2% of total)

ival-sub: 2.0ms (5.2% of total)

ival-sqrt: 2.0ms (5.2% of total)

adjust: 0.0ms (0% of total)

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

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

exact: 0.0ms (0% of total)

series37.0ms (1.4%)

Memory

-47.5MiB live, 9.2MiB allocated; 12ms collecting garbage

Counts

10 → 24

Calls

Call 1

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

Outputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
-1/2
(- (* -1/8 (pow x 2)) 1/2)
(* -1/8 (pow x 2))
(sin (acos x))
(acos x)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (- 1 (* x x))) (+ (* (- (* -1/8 (* x x)) 1/2) (* x x)) 1) (- (* -1/8 (* x x)) 1/2) (* -1/8 (* x x)) (sin (acos x)) (acos x))
1.0ms	x	@	-inf	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (- 1 (* x x))) (+ (* (- (* -1/8 (* x x)) 1/2) (* x x)) 1) (- (* -1/8 (* x x)) 1/2) (* -1/8 (* x x)) (sin (acos x)) (acos x))
1.0ms	x	@	0	((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (- 1 (* x x))) (+ (* (- (* -1/8 (* x x)) 1/2) (* x x)) 1) (- (* -1/8 (* x x)) 1/2) (* -1/8 (* x x)) (sin (acos x)) (acos x))

Time

Variable

Point

Expression

3.0ms

inf

((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (- 1 (* x x))) (+ (* (- (* -1/8 (* x x)) 1/2) (* x x)) 1) (- (* -1/8 (* x x)) 1/2) (* -1/8 (* x x)) (sin (acos x)) (acos x))

1.0ms

-inf

((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (- 1 (* x x))) (+ (* (- (* -1/8 (* x x)) 1/2) (* x x)) 1) (- (* -1/8 (* x x)) 1/2) (* -1/8 (* x x)) (sin (acos x)) (acos x))

1.0ms

((sqrt (- 1 (* x x))) (sqrt (- 1 (* x x))) (+ (* (* x x) -1/2) 1) (* x x) (sqrt (- 1 (* x x))) (+ (* (- (* -1/8 (* x x)) 1/2) (* x x)) 1) (- (* -1/8 (* x x)) 1/2) (* -1/8 (* x x)) (sin (acos x)) (acos x))

simplify150.0ms (5.6%)

Memory

44.8MiB live, 177.9MiB allocated; 20ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	274
1	189	270
2	630	257
3	2085	246
4	7602	246
0	8245	233

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(pow x 2)
-1/2
(- (* -1/8 (pow x 2)) 1/2)
(* -1/8 (pow x 2))
(sin (acos x))
(acos x)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

Outputs
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
(fma.f64 (-.f64 (.f64 (.f64 (-.f64 (.f64 #s(literal -1/16 binary64) (.f64 x x)) #s(literal 1/8 binary64)) x) x) #s(literal 1/2 binary64)) (*.f64 x x) #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
-1/2
#s(literal -1/2 binary64)
(- (* -1/8 (pow x 2)) 1/2)
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(sin (acos x))
(sin.f64 (acos.f64 x))
(acos x)
(acos.f64 x)
(* x (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x)))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) x (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64)))) x (/.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 4 binary64))) x (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(* -1/2 (pow x 2))
(.f64 (.f64 x x) #s(literal -1/2 binary64))
(* (pow x 2) (- (/ 1 (pow x 2)) 1/2))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) x) x)
(* -1/8 (pow x 4))
(*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/8 binary64))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/8 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x))) (pow.f64 x #s(literal 4 binary64)))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(* -1 (* x (sqrt -1)))
(*.f64 (neg.f64 x) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) x (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) x))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(fma.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) x (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) x (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))
(fma.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 #s(literal -1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 x) (/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) x (/.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 #s(literal -1 binary64))))

rewrite153.0ms (5.8%)

Memory

-32.8MiB live, 263.4MiB allocated; 35ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	78
0	27	69
1	102	69
2	742	69
0	8031	69

Stop Event

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

Counts

10 → 229

Calls

Call 1

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

Outputs
#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))
#s(approx (sqrt (- 1 (* x x))) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64)) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1/64 binary64) (pow.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/16 binary64) (.f64 (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64))) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64)) (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) (/.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))
(.f64 (fma.f64 #s(literal -1/2 binary64) (.f64 x x) #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))))) (.f64 (pow.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64))) (pow.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))))) (.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)))) (-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) (fma.f64 (pow.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))) (pow.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (-.f64 (.f64 (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64))) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64)))) (pow.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 x x) #s(literal 1 binary64))) #s(literal -1 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal -1 binary64)))) (neg.f64 (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/8 binary64) #s(literal 1 binary64)))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64) #s(literal 1 binary64))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 x x) #s(literal 1 binary64))))
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(/.f64 (-.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 (asin.f64 x) #s(literal 3 binary64))) (fma.f64 (asin.f64 x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 x)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 x))) (/.f64 (pow.f64 (asin.f64 x) #s(literal 2 binary64)) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 x))))
(-.f64 (/.f64 (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 3 binary64)) (fma.f64 (asin.f64 x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 x)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (asin.f64 x) #s(literal 3 binary64)) (fma.f64 (asin.f64 x) (+.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 x)) (pow.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (asin.f64 x))
(+.f64 (-.f64 (/.f64 (PI.f64) #s(literal 2 binary64)) (/.f64 (PI.f64) #s(literal 2 binary64))) (acos.f64 x))
(acos.f64 x)

eval55.0ms (2.1%)

Memory: 31.2MiB live, 123.8MiB allocated; 5ms collecting garbage
Compiler: Compiled 9 600 to 1 090 computations (88.6% saved)

prune50.0ms (1.9%)

Memory

-24.9MiB live, 24.6MiB allocated; 6ms collecting garbage

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	285	5	290

Accuracy

100.0%

Counts

290 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	100.0%	(sin.f64 (acos.f64 x))
▶	99.8%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
✓	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	99.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 48 to 37 computations (22.9% saved)

simplify51.0ms (1.9%)

Memory

3.2MiB live, 48.6MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
0	16	42
1	32	42
2	101	42
3	341	42
4	1055	42
5	1733	42
6	1762	42
7	1793	42
8	1808	42
9	1808	42
0	1808	42

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize44.0ms (1.6%)

Memory

4.8MiB live, 50.0MiB allocated; 5ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64))
accuracy	0.0	(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	0.1495469356347079	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 35 to 13 computations (62.9% saved)

Precisions

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

ival-mult: 5.0ms (45.5% of total)

ival-add: 2.0ms (18.2% of total)

ival-sqrt: 2.0ms (18.2% of total)

ival-sub: 1.0ms (9.1% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

series2.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated; 0ms collecting garbage

Counts

4 → 20

Calls

Call 1

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

Outputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
-1/2
(- (* -1/8 (pow x 2)) 1/2)
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1/8 (pow x 2))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

0.0ms

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

simplify141.0ms (5.3%)

Memory

-5.8MiB live, 139.1MiB allocated; 17ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	253
1	185	249
2	611	236
3	2054	225
4	7535	225
0	8169	212

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 20

Calls

Call 1

Inputs
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* -1/8 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (- (* -1/16 (pow x 2)) 1/8)) 1/2)))
-1/2
(- (* -1/8 (pow x 2)) 1/2)
(pow x 2)
(* x (sqrt -1))
(* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1))))))
(* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3)))))
(* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1/8 (pow x 4))
(* -1 (* (pow x 4) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 4) (- (/ 1 (pow x 4)) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1/8 (pow x 2))
(* -1 (* (pow x 2) (+ 1/8 (* 1/2 (/ 1 (pow x 2))))))
(* -1 (* x (sqrt -1)))
(* -1 (* x (+ (sqrt -1) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))))
(* -1 (* x (- (+ (sqrt -1) (/ 1/2 (* (pow x 2) (sqrt -1)))) (/ 1/8 (* (pow x 4) (pow (sqrt -1) 3))))))
(* -1 (* x (- (+ (sqrt -1) (+ (/ 1/2 (* (pow x 2) (sqrt -1))) (* 1/16 (/ 1 (* (pow x 6) (pow (sqrt -1) 5)))))) (* 1/8 (/ 1 (* (pow x 4) (pow (sqrt -1) 3)))))))

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

rewrite235.0ms (8.8%)

Memory

-6.5MiB live, 179.5MiB allocated; 44ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	38
0	16	35
1	77	35
2	568	35
3	6690	35
0	8077	35

Stop Event

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

Counts

4 → 170

Calls

Call 1

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

Outputs
#s(approx (sqrt (- 1 (* x x))) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (-.f64 (.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) x) #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)) #s(literal 2 binary64)))) (-.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (*.f64 x x) #s(literal 1/2 binary64)) x) x)))
(.f64 (/.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) x) #s(literal 6 binary64)))) (fma.f64 (fma.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) (.f64 x x) #s(literal 1/2 binary64)) x) x #s(literal 1 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64))) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) x) #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (*.f64 x x) #s(literal 1 binary64)))
(.f64 (/.f64 (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (fma.f64 (pow.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (fma.f64 (.f64 (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64)) x) #s(literal 1 binary64)))
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(fma.f64 (/.f64 (.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/262144 binary64) (pow.f64 x #s(literal 12 binary64)) (pow.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))) #s(literal 3 binary64)))) (fma.f64 #s(literal 1/4096 binary64) (pow.f64 x #s(literal 8 binary64)) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x)))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))))
(fma.f64 (*.f64 #s(literal 1/8 binary64) x) (neg.f64 x) #s(literal -1/2 binary64))
(fma.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal 3/2 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))))
(fma.f64 (pow.f64 (.f64 #s(literal -1/8 binary64) x) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (*.f64 x x))))))
(fma.f64 #s(literal -1/512 binary64) (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) x) x #s(literal -1/2 binary64))
(fma.f64 (pow.f64 x #s(literal 6 binary64)) (/.f64 #s(literal -1/512 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))))
(fma.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (*.f64 x x))))))
(fma.f64 (neg.f64 x) (*.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (*.f64 x x))))))
(fma.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/8 binary64) #s(literal -1/2 binary64))
(fma.f64 #s(literal -1/8 binary64) (*.f64 x x) #s(literal -1/2 binary64))
(fma.f64 x (*.f64 #s(literal -1/8 binary64) x) #s(literal -1/2 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))
(-.f64 (/.f64 #s(literal 1/4 binary64) (-.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))) (/.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/8 binary64)))))
(-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 #s(literal 1/64 binary64) (-.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)))) (/.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (*.f64 x x) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))))
(-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/8 binary64) (.f64 x x)))
(+.f64 (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 (.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (*.f64 x x))))))
(+.f64 (/.f64 (.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x))))) (/.f64 #s(literal -1/8 binary64) (fma.f64 #s(literal 1/64 binary64) (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1/4 binary64) (.f64 #s(literal 1/16 binary64) (*.f64 x x))))))
(+.f64 (.f64 (.f64 x x) #s(literal -1/8 binary64)) #s(literal -1/2 binary64))
(+.f64 #s(literal -1/2 binary64) (.f64 (neg.f64 (.f64 #s(literal 1/8 binary64) x)) x))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 x x)
(.f64 #s(literal 1 binary64) (.f64 x x))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 x) x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 x) x))
(fabs.f64 (*.f64 x x))
(exp.f64 (*.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 (neg.f64 x)) #s(literal 2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval61.0ms (2.3%)

Memory: -0.7MiB live, 44.0MiB allocated; 6ms collecting garbage
Compiler: Compiled 7 821 to 822 computations (89.5% saved)

prune5.0ms (0.2%)

Memory

13.2MiB live, 13.2MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	207	5	212

Accuracy

100.0%

Counts

212 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	100.0%	(sin.f64 (acos.f64 x))
✓	99.8%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x x) #s(literal -1/2 binary64)) (.f64 x x) #s(literal 1 binary64)))
✓	99.6%	#s(approx (sqrt (- 1 (* x x))) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) #s(literal 1 binary64)))
✓	99.0%	#s(approx (sqrt (- 1 (* x x))) #s(literal 1 binary64))

Compiler

Compiled 115 to 61 computations (47% saved)

regimes7.0ms (0.3%)

Memory

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

Counts

6 → 1

Calls

Call 1

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

Outputs
(sin.f64 (acos.f64 x))

Calls

4 calls:

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

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes6.0ms (0.2%)

Memory

11.3MiB live, 11.3MiB allocated; 0ms collecting garbage

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes9.0ms (0.3%)

Memory

-37.7MiB live, 8.5MiB allocated; 4ms collecting garbage

Counts

2 → 1

Calls

Call 1

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

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

Calls

4 calls:

5.0ms	(*.f64 x x)
1.0ms	x
1.0ms	(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))
1.0ms	(-.f64 #s(literal 1 binary64) (*.f64 x x))

Results

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

Compiler

Compiled 15 to 12 computations (20% saved)

regimes4.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.0%	1	`(*.f64 x x)`
99.0%	1	`(-.f64 #s(literal 1 binary64) (*.f64 x x))`
99.0%	1	`(sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))`
99.0%	1	`x`

Compiler

Compiled 15 to 12 computations (20% saved)

simplify11.0ms (0.4%)

Memory

15.3MiB live, 15.3MiB allocated; 0ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	27	30
2	56	30
3	84	30
4	99	30

Stop Event

1×

saturated

Calls

Call 1

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

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

derivations248.0ms (9.3%)

Memory

12.2MiB live, 259.6MiB allocated; 38ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	220
1	156	219
2	475	203
3	1620	192
4	5992	192
0	8180	181
0	5	14
0	8	11
1	38	11
2	241	11
3	2203	11
0	8263	10

Stop Event

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

Compiler

Compiled 30 to 15 computations (50% saved)

preprocess40.0ms (1.5%)

Memory: 0.3MiB live, 46.3MiB allocated; 5ms collecting garbage
Remove: (abs x)
Compiler: Compiled 84 to 52 computations (38.1% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze2.0ms (0.1%)

sample677.0ms (25.4%)

explain174.0ms (6.5%)

preprocess58.0ms (2.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.2%)

localize15.0ms (0.6%)

series3.0ms (0.1%)

simplify147.0ms (5.5%)

rewrite161.0ms (6.1%)

eval33.0ms (1.2%)

prune4.0ms (0.1%)

simplify15.0ms (0.5%)

localize59.0ms (2.2%)

series37.0ms (1.4%)

simplify150.0ms (5.6%)

rewrite153.0ms (5.8%)

eval55.0ms (2.1%)

prune50.0ms (1.9%)

simplify51.0ms (1.9%)

localize44.0ms (1.6%)

series2.0ms (0.1%)

simplify141.0ms (5.3%)

rewrite235.0ms (8.8%)

eval61.0ms (2.3%)

prune5.0ms (0.2%)

regimes7.0ms (0.3%)

regimes6.0ms (0.2%)

regimes9.0ms (0.3%)

regimes4.0ms (0.1%)

simplify11.0ms (0.4%)

derivations248.0ms (9.3%)

preprocess40.0ms (1.5%)

end0.0ms (0%)

Profiling