Metrics for Linear.Quaternion:$ctan from linear-1.19.1.3

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze71.0ms (5.2%)

Memory

8.2MiB live, 88.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
25%	25%	74.9%	0.1%	0%	0%	0%	4
37.5%	37.4%	62.4%	0.1%	0%	0%	0%	5
37.5%	37.4%	62.4%	0.1%	0%	0%	0%	6
56.3%	56.2%	43.7%	0.1%	0%	0%	0%	7
65.6%	65.5%	34.3%	0.1%	0%	0%	0%	8
65.6%	65.5%	34.3%	0.1%	0%	0%	0%	9
76.6%	76.5%	23.4%	0.1%	0%	0%	0%	10
82%	81.9%	17.9%	0.1%	0%	0%	0%	11
82%	81.9%	17.9%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 9 computations (10% saved)

sample939.0ms (69.6%)

Memory

7.5MiB live, 1 117.6MiB allocated

Samples

489.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 297.0ms

ival-div: 131.0ms (44.1% of total)

ival-cosh: 104.0ms (35% of total)

ival-mult: 52.0ms (17.5% of total)

ival-true: 6.0ms (2% of total)

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

Bogosity

explain84.0ms (6.2%)

Memory

-12.5MiB live, 109.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
25	-	-	`(*.f64 (cosh.f64 x) (/.f64 y x))`
11	-	-	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
0	-	-	`(/.f64 y x)`
0	-	-	`y`
0	-	-	`(cosh.f64 x)`
0	-	-	`z`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`*.f64`	`(*.f64 (cosh.f64 x) (/.f64 y x))`	*ou**	25	0
↳	`(cosh.f64 x)`	overflow	137
↳	`(/.f64 y x)`	underflow	25
`/.f64`	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`	o/n	11	0
↳	`(cosh.f64 x)`	overflow	137
↳	`(/.f64 y x)`	overflow	33
↳	`(*.f64 (cosh.f64 x) (/.f64 y x))`	overflow	170

Confusion

	Predicted +	Predicted -
+	36	0
-	0	220

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	36	0	0
-	0	0	220

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	220
1	36

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

46.0ms

512×

valid

Compiler

Compiled 78 to 32 computations (59% saved)

Precisions

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

ival-div: 22.0ms (70% of total)

ival-cosh: 6.0ms (19.1% of total)

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

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

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

preprocess3.0ms (0.2%)

Memory

6.0MiB live, 6.0MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Outputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 8 to 7 computations (12.5% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	86.1%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 y x)
cost-diff	0	(cosh.f64 x)
cost-diff	0	(*.f64 (cosh.f64 x) (/.f64 y x))
cost-diff	0	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Calls

Call 1

Inputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
(*.f64 (cosh.f64 x) (/.f64 y x))
(cosh.f64 x)
x
(/.f64 y x)
y
z

Outputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
(*.f64 (cosh.f64 x) (/.f64 y x))
(cosh.f64 x)
x
(/.f64 y x)
y
z

localize26.0ms (1.9%)

Memory

-6.4MiB live, 31.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	0.0	(cosh.f64 x)
accuracy	2.615071554907858	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
accuracy	5.699189851622882	(*.f64 (cosh.f64 x) (/.f64 y x))

Samples

21.0ms

256×

valid

Compiler

Compiled 46 to 16 computations (65.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (48.7% of total)

ival-cosh: 3.0ms (36.5% of total)

ival-mult: 1.0ms (12.2% of total)

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

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

series22.0ms (1.6%)

Memory

-17.6MiB live, 26.5MiB allocated

Counts

4 → 15

Calls

Call 1

Inputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
(*.f64 (cosh.f64 x) (/.f64 y x))
(cosh.f64 x)
(/.f64 y x)

Outputs
(/ y (* x z))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
(/ y x)
(/ (+ y (* 1/2 (* (pow x 2) y))) x)
(/ (+ y (* (pow x 2) (+ (* 1/24 (* (pow x 2) y)) (* 1/2 y)))) x)
(/ (+ y (* (pow x 2) (+ (* 1/2 y) (* (pow x 2) (+ (* 1/720 (* (pow x 2) y)) (* 1/24 y)))))) x)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) (* x z)))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) x))
(* 1/2 (+ (exp x) (/ 1 (exp x))))

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	y	@	inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
3.0ms	y	@	0	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
3.0ms	x	@	-inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
3.0ms	x	@	inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
2.0ms	y	@	-inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Counts

15 → 4

Calls

Call 1

Inputs
(/ y (* x z))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
(/ y x)
(/ (+ y (* 1/2 (* (pow x 2) y))) x)
(/ (+ y (* (pow x 2) (+ (* 1/24 (* (pow x 2) y)) (* 1/2 y)))) x)
(/ (+ y (* (pow x 2) (+ (* 1/2 y) (* (pow x 2) (+ (* 1/720 (* (pow x 2) y)) (* 1/24 y)))))) x)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) (* x z)))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) x))
(* 1/2 (+ (exp x) (/ 1 (exp x))))

Outputs
(/ y (* x z))
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(*.f64 (cosh.f64 x) (/.f64 y x))
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
(cosh.f64 x)
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
(/.f64 y x)

rewrite0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Counts

4 → 4

Calls

Call 1

Inputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
(*.f64 (cosh.f64 x) (/.f64 y x))
(cosh.f64 x)
(/.f64 y x)

Outputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
(*.f64 (cosh.f64 x) (/.f64 y x))
(cosh.f64 x)
(/.f64 y x)

eval1.0ms (0.1%)

Memory: 1.6MiB live, 1.6MiB allocated
Compiler: Compiled 87 to 15 computations (82.8% saved)

prune1.0ms (0.1%)

Memory

2.9MiB live, 2.9MiB allocated

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	5	3	8
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	5	4	9

Accuracy

91.7%

Counts

9 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	86.1%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
▶	6.2%	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
▶	26.3%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
▶	29.2%	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Compiler

Compiled 46 to 36 computations (21.7% saved)

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 y x)
cost-diff	0	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
cost-diff	0	(/.f64 y x)
cost-diff	0	(cosh.f64 x)
cost-diff	0	(*.f64 (cosh.f64 x) (/.f64 y x))
cost-diff	0	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
cost-diff	0	(cosh.f64 x)
cost-diff	0	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
(cosh.f64 x)
x
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
(*.f64 (cosh.f64 x) (/.f64 y x))
(cosh.f64 x)
x
(/.f64 y x)
y
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
(/.f64 y x)
y
x

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
(cosh.f64 x)
x
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
(*.f64 (cosh.f64 x) (/.f64 y x))
(cosh.f64 x)
x
(/.f64 y x)
y
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
(/.f64 y x)
y
x

localize27.0ms (2%)

Memory

-2.1MiB live, 35.4MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	60.058295868306566	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
accuracy	0.0	(/.f64 y x)
accuracy	0.0	(cosh.f64 x)
accuracy	5.699189851622882	(*.f64 (cosh.f64 x) (/.f64 y x))
accuracy	44.148360590085126	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
accuracy	0.0	(cosh.f64 x)
accuracy	45.32991879493934	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Samples

21.0ms

256×

valid

Compiler

Compiled 106 to 22 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (48.3% of total)

ival-cosh: 3.0ms (36.3% of total)

ival-mult: 1.0ms (12.1% of total)

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

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

series10.0ms (0.7%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

6 → 15

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
(cosh.f64 x)
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
(*.f64 (cosh.f64 x) (/.f64 y x))
(/.f64 y x)
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))

Outputs
(/ y (* x z))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ y x)
(/ (+ y (* 1/2 (* (pow x 2) y))) x)
(/ (+ y (* (pow x 2) (+ (* 1/24 (* (pow x 2) y)) (* 1/2 y)))) x)
(/ (+ y (* (pow x 2) (+ (* 1/2 y) (* (pow x 2) (+ (* 1/720 (* (pow x 2) y)) (* 1/24 y)))))) x)
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) (* x z)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) x))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	y	@	-inf	((/ (* (cosh x) (/ y x)) z) (cosh x) (/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (/ y x) (/ (* (cosh x) (/ y x)) z))
1.0ms	x	@	-inf	((/ (* (cosh x) (/ y x)) z) (cosh x) (/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (/ y x) (/ (* (cosh x) (/ y x)) z))
1.0ms	y	@	inf	((/ (* (cosh x) (/ y x)) z) (cosh x) (/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (/ y x) (/ (* (cosh x) (/ y x)) z))
1.0ms	y	@	0	((/ (* (cosh x) (/ y x)) z) (cosh x) (/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (/ y x) (/ (* (cosh x) (/ y x)) z))
1.0ms	x	@	inf	((/ (* (cosh x) (/ y x)) z) (cosh x) (/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (/ y x) (/ (* (cosh x) (/ y x)) z))

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Counts

15 → 6

Calls

Call 1

Inputs
(/ y (* x z))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(/ y x)
(/ (+ y (* 1/2 (* (pow x 2) y))) x)
(/ (+ y (* (pow x 2) (+ (* 1/24 (* (pow x 2) y)) (* 1/2 y)))) x)
(/ (+ y (* (pow x 2) (+ (* 1/2 y) (* (pow x 2) (+ (* 1/720 (* (pow x 2) y)) (* 1/24 y)))))) x)
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) (* x z)))
(* 1/2 (+ (exp x) (/ 1 (exp x))))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) x))

Outputs
(/ y (* x z))
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(cosh.f64 x)
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
(*.f64 (cosh.f64 x) (/.f64 y x))
1
(/.f64 y x)
(+ 1 (* 1/2 (pow x 2)))
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))

rewrite0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Counts

6 → 6

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
(cosh.f64 x)
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
(*.f64 (cosh.f64 x) (/.f64 y x))
(/.f64 y x)
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
(cosh.f64 x)
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
(*.f64 (cosh.f64 x) (/.f64 y x))
(/.f64 y x)
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))

eval1.0ms (0.1%)

Memory: 2.7MiB live, 2.7MiB allocated
Compiler: Compiled 236 to 23 computations (90.3% saved)

prune3.0ms (0.2%)

Memory

5.0MiB live, 5.0MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	13	1	14
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	13	5	18

Accuracy

91.7%

Counts

18 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	86.1%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
✓	6.2%	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
✓	26.3%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
▶	12.0%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
✓	29.2%	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 y x)
cost-diff	0	#s(approx (cosh x) (/.f64 y x))
cost-diff	0	(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
cost-diff	0	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
#s(approx (cosh x) (/.f64 y x))
(/.f64 y x)
y
x

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
#s(approx (cosh x) (/.f64 y x))
(/.f64 y x)
y
x

localize25.0ms (1.8%)

Memory

-0.4MiB live, 37.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	5.699189851622882	(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
accuracy	44.148360590085126	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
accuracy	62.489820031237635	#s(approx (cosh x) (/.f64 y x))

Samples

19.0ms

256×

valid

Compiler

Compiled 63 to 20 computations (68.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 4.0ms (48.3% of total)

ival-cosh: 3.0ms (36.2% of total)

ival-mult: 1.0ms (12.1% of total)

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

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

series19.0ms (1.4%)

Memory

-17.4MiB live, 19.4MiB allocated

Counts

4 → 15

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
#s(approx (cosh x) (/.f64 y x))
(/.f64 y x)

Outputs
(/ y (* x z))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
(/ y x)
(/ (+ y (* 1/2 (* (pow x 2) y))) x)
(/ (+ y (* (pow x 2) (+ (* 1/24 (* (pow x 2) y)) (* 1/2 y)))) x)
(/ (+ y (* (pow x 2) (+ (* 1/2 y) (* (pow x 2) (+ (* 1/720 (* (pow x 2) y)) (* 1/24 y)))))) x)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) (* x z)))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) x))
(* 1/2 (+ (exp x) (/ 1 (exp x))))

Calls

9 calls:

Time	Variable		Point	Expression
11.0ms	x	@	-inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
1.0ms	y	@	-inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
1.0ms	y	@	inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
1.0ms	y	@	0	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))
1.0ms	x	@	inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Counts

15 → 4

Calls

Call 1

Inputs
(/ y (* x z))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
(/ y x)
(/ (+ y (* 1/2 (* (pow x 2) y))) x)
(/ (+ y (* (pow x 2) (+ (* 1/24 (* (pow x 2) y)) (* 1/2 y)))) x)
(/ (+ y (* (pow x 2) (+ (* 1/2 y) (* (pow x 2) (+ (* 1/720 (* (pow x 2) y)) (* 1/24 y)))))) x)
1
(+ 1 (* 1/2 (pow x 2)))
(+ 1 (* (pow x 2) (+ 1/2 (* 1/24 (pow x 2)))))
(+ 1 (* (pow x 2) (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/720 (pow x 2)))))))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) (* x z)))
(* 1/2 (/ (* y (+ (exp x) (/ 1 (exp x)))) x))
(* 1/2 (+ (exp x) (/ 1 (exp x))))

Outputs
(/ y (* x z))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
(/ (+ (* 1/2 (/ (* (pow x 2) y) z)) (/ y z)) x)
(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
(/ (+ (* (pow x 2) (+ (* 1/24 (/ (* (pow x 2) y) z)) (* 1/2 (/ y z)))) (/ y z)) x)
#s(approx (cosh x) (/.f64 y x))
(/ (+ (* (pow x 2) (+ (* 1/2 (/ y z)) (* (pow x 2) (+ (* 1/720 (/ (* (pow x 2) y) z)) (* 1/24 (/ y z)))))) (/ y z)) x)
(/.f64 y x)

rewrite0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Counts

4 → 4

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
#s(approx (cosh x) (/.f64 y x))
(/.f64 y x)

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
#s(approx (cosh x) (/.f64 y x))
(/.f64 y x)

eval1.0ms (0.1%)

Memory: 1.9MiB live, 1.9MiB allocated
Compiler: Compiled 150 to 14 computations (90.7% saved)

prune3.0ms (0.2%)

Memory

6.6MiB live, 6.6MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	8	0	8
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	8	5	13

Accuracy

91.7%

Counts

13 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	86.1%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
✓	6.2%	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
✓	26.3%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
✓	12.0%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
✓	29.2%	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Compiler

Compiled 130 to 64 computations (50.8% saved)

regimes24.0ms (1.8%)

Memory

-24.2MiB live, 24.2MiB allocated

Counts

5 → 2

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Outputs
(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Calls

5 calls:

15.0ms	y
2.0ms	z
2.0ms	x
2.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
2.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Results

Accuracy	Segments	Branch
86.1%	1	`x`
86.1%	1	`y`
86.1%	1	`z`
91.6%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
91.6%	2	`(*.f64 (cosh.f64 x) (/.f64 y x))`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

regimes10.0ms (0.7%)

Memory

23.0MiB live, 23.0MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))

Calls

5 calls:

2.0ms	x
2.0ms	z
2.0ms	y
2.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
2.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Results

Accuracy	Segments	Branch
40.1%	2	`z`
37.2%	3	`x`
31.5%	2	`y`
40.1%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
31.8%	2	`(*.f64 (cosh.f64 x) (/.f64 y x))`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

regimes14.0ms (1%)

Memory

-25.5MiB live, 12.6MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Calls

3 calls:

2.0ms	x
2.0ms	z
1.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Results

Accuracy	Segments	Branch
37.2%	3	`x`
31.8%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
29.2%	1	`z`

Compiler

Compiled 10 to 13 computations (-30% saved)

regimes7.0ms (0.5%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))

Calls

5 calls:

1.0ms	x
1.0ms	y
1.0ms	z
1.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))
1.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Results

Accuracy	Segments	Branch
12.0%	1	`z`
12.0%	1	`y`
12.0%	1	`(*.f64 (cosh.f64 x) (/.f64 y x))`
14.4%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
12.0%	1	`x`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

regimes6.0ms (0.4%)

Memory

15.0MiB live, 15.0MiB allocated

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))

Outputs
#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))

Calls

5 calls:

1.0ms	z
1.0ms	y
1.0ms	x
1.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
1.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

Results

Accuracy	Segments	Branch
6.2%	1	`(*.f64 (cosh.f64 x) (/.f64 y x))`
6.2%	1	`x`
6.2%	1	`y`
6.2%	1	`z`
6.2%	1	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	+inf	NaN

Compiler

Compiled 11 to 13 computations (-18.2% saved)

bsearch14.0ms (1%)

Memory

-19.5MiB live, 19.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.9516922324360263e-299	3.459552047438595e-298

Samples

6.0ms

112×

valid

Compiler

Compiled 193 to 167 computations (13.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-div: 2.0ms (54.8% of total)

ival-mult: 1.0ms (27.4% of total)

ival-cosh: 1.0ms (27.4% of total)

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

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

bsearch30.0ms (2.2%)

Memory

3.5MiB live, 41.5MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.0001696041459521507	0.006814345135216369
13.0ms	-2.0737058883172802e-72	-8.177379796257035e-81

Samples

15.0ms

256×

valid

Compiler

Compiled 491 to 365 computations (25.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 4.0ms (46.7% of total)

ival-cosh: 3.0ms (35% of total)

ival-mult: 1.0ms (11.7% of total)

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

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

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-7.745913411683186e-112	-3.4956671758899257e-149

Compiler

Compiled 11 to 13 computations (-18.2% saved)

simplify4.0ms (0.3%)

Memory: 9.0MiB live, 9.0MiB allocated

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze71.0ms (5.2%)

sample939.0ms (69.6%)

explain84.0ms (6.2%)

preprocess3.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize26.0ms (1.9%)

series22.0ms (1.6%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify0.0ms (0%)

localize27.0ms (2%)

series10.0ms (0.7%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune3.0ms (0.2%)

simplify0.0ms (0%)

localize25.0ms (1.8%)

series19.0ms (1.4%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune3.0ms (0.2%)

regimes24.0ms (1.8%)

regimes10.0ms (0.7%)

regimes14.0ms (1%)

regimes7.0ms (0.5%)

regimes6.0ms (0.4%)

bsearch0.0ms (0%)

bsearch14.0ms (1%)

bsearch30.0ms (2.2%)

bsearch0.0ms (0%)

simplify4.0ms (0.3%)

end0.0ms (0%)

Profiling