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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze73.0ms (5.2%)

Memory

1.4MiB live, 128.4MiB 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)

sample980.0ms (70.2%)

Memory

-26.6MiB live, 1 045.6MiB allocated

Samples

479.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 306.0ms

ival-div: 142.0ms (46.5% of total)

ival-cosh: 106.0ms (34.7% of total)

ival-mult: 48.0ms (15.7% of total)

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

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

Bogosity

explain81.0ms (5.8%)

Memory

-13.7MiB live, 108.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
21	-	-	`(*.f64 (cosh.f64 x) (/.f64 y x))`
9	-	-	`(/.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**	21	0
↳	`(cosh.f64 x)`	overflow	122
↳	`(/.f64 y x)`	underflow	21
`/.f64`	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`	o/n	9	0
↳	`(cosh.f64 x)`	overflow	122
↳	`(/.f64 y x)`	overflow	28
↳	`(*.f64 (cosh.f64 x) (/.f64 y x))`	overflow	150

Confusion

	Predicted +	Predicted -
+	30	0
-	0	226

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	30	0	0
-	0	0	226

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	226
1	30

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms

512×

valid

Compiler

Compiled 78 to 32 computations (59% saved)

Precisions

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

ival-cosh: 9.0ms (45.8% of total)

ival-div: 7.0ms (35.6% of total)

ival-mult: 3.0ms (15.3% of total)

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

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

preprocess3.0ms (0.2%)

Memory

6.1MiB live, 6.1MiB 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: 0.1MiB live, 0.1MiB 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
▶	88.3%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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

localize25.0ms (1.8%)

Memory

-7.3MiB live, 30.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	0.00390625	(cosh.f64 x)
accuracy	2.2058301000042	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
accuracy	5.062464909113499	(*.f64 (cosh.f64 x) (/.f64 y x))

Samples

15.0ms

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: 3.0ms (37.7% of total)

ival-cosh: 3.0ms (37.7% of total)

ival-mult: 1.0ms (12.6% of total)

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

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

series22.0ms (1.5%)

Memory

-10.5MiB live, 26.7MiB 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
5.0ms	z	@	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

3.0MiB live, 3.0MiB 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

92.3%

Counts

9 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	88.3%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
▶	7.1%	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
▶	30.8%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
▶	25.1%	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Compiler

Compiled 46 to 36 computations (21.7% saved)

simplify0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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

localize35.0ms (2.5%)

Memory

-15.1MiB live, 36.9MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	59.434625706966614	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
accuracy	0.0	(/.f64 y x)
accuracy	0.00390625	(cosh.f64 x)
accuracy	5.062464909113499	(*.f64 (cosh.f64 x) (/.f64 y x))
accuracy	40.56681822059741	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
accuracy	0.00390625	(cosh.f64 x)
accuracy	47.95073704541013	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Samples

29.0ms

256×

valid

Compiler

Compiled 106 to 22 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-cosh: 15.0ms (72.3% of total)

ival-div: 4.0ms (19.3% of total)

ival-mult: 1.0ms (4.8% of total)

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

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

series10.0ms (0.7%)

Memory

23.8MiB live, 23.8MiB 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

0.8MiB live, 0.8MiB 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: 3.2MiB live, 3.2MiB allocated
Compiler: Compiled 236 to 23 computations (90.3% saved)

prune9.0ms (0.6%)

Memory

-31.7MiB live, 5.8MiB 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

92.3%

Counts

18 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	88.3%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
✓	7.1%	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
✓	30.8%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
▶	11.4%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
✓	25.1%	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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

localize20.0ms (1.4%)

Memory

33.8MiB live, 33.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 y x)
accuracy	5.062464909113499	(*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x))
accuracy	40.56681822059741	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
accuracy	62.4080238975044	#s(approx (cosh x) (/.f64 y x))

Samples

15.0ms

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: 3.0ms (38.5% of total)

ival-cosh: 3.0ms (38.5% of total)

ival-mult: 1.0ms (12.8% of total)

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

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

series20.0ms (1.4%)

Memory

-17.9MiB live, 19.1MiB 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
12.0ms	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	@	0	((/ (* (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	x	@	inf	((/ (* (cosh x) (/ y x)) z) (* (cosh x) (/ y x)) (cosh x) (/ y x))

simplify0.0ms (0%)

Memory

0.8MiB live, 0.8MiB 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: 2.0MiB live, 2.0MiB allocated
Compiler: Compiled 150 to 14 computations (90.7% saved)

prune3.0ms (0.2%)

Memory

6.5MiB live, 6.5MiB 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

92.3%

Counts

13 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	88.3%	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
✓	7.1%	#s(approx (/ (* (cosh x) (/ y x)) z) (/.f64 y x))
✓	30.8%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 (cosh.f64 x) (/.f64 y x)))
✓	11.4%	#s(approx (/ (* (cosh x) (/ y x)) z) (*.f64 #s(approx (cosh x) (/.f64 y x)) (/.f64 y x)))
✓	25.1%	#s(approx (/ (* (cosh x) (/ y x)) z) (cosh.f64 x))

Compiler

Compiled 130 to 64 computations (50.8% saved)

regimes21.0ms (1.5%)

Memory

-11.7MiB live, 26.0MiB 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:

11.0ms	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
88.3%	1	`x`
88.3%	1	`y`
88.3%	1	`z`
92.2%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
92.2%	2	`(*.f64 (cosh.f64 x) (/.f64 y x))`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

regimes11.0ms (0.8%)

Memory

23.6MiB live, 23.6MiB 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	z
2.0ms	y
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
34.7%	3	`y`
35.6%	4	`x`
41.1%	2	`z`
39.9%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
34.7%	2	`(*.f64 (cosh.f64 x) (/.f64 y x))`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

regimes13.0ms (0.9%)

Memory

-26.5MiB live, 21.0MiB 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

5 calls:

5.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
2.0ms	z
2.0ms	x
2.0ms	y
2.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

Results

Accuracy	Segments	Branch
32.5%	3	`x`
25.1%	1	`y`
25.1%	1	`(*.f64 (cosh.f64 x) (/.f64 y x))`
27.9%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
25.1%	1	`z`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

regimes8.0ms (0.5%)

Memory

18.4MiB live, 18.4MiB 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	y
1.0ms	x
1.0ms	z
1.0ms	(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)
1.0ms	(*.f64 (cosh.f64 x) (/.f64 y x))

Results

Accuracy	Segments	Branch
11.4%	1	`(*.f64 (cosh.f64 x) (/.f64 y x))`
11.4%	1	`z`
11.4%	1	`y`
14.1%	2	`(/.f64 (*.f64 (cosh.f64 x) (/.f64 y x)) z)`
11.4%	1	`x`

Compiler

Compiled 17 to 22 computations (-29.4% saved)

regimes8.0ms (0.6%)

Memory

-23.5MiB live, 15.3MiB 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:

4.0ms	y
1.0ms	x
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
7.1%	1	`(*.f64 (cosh.f64 x) (/.f64 y x))`
7.1%	1	`x`
7.1%	1	`y`
7.1%	1	`z`
7.1%	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)

bsearch16.0ms (1.1%)

Memory

24.9MiB live, 24.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	-7.912880292590428e-303	1.856832285413663e-304

Samples

9.0ms

160×

valid

Compiler

Compiled 271 to 233 computations (14% saved)

Precisions

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

ival-div: 2.0ms (40% of total)

ival-cosh: 2.0ms (40% of total)

ival-mult: 1.0ms (20% of total)

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

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

bsearch26.0ms (1.9%)

Memory

-2.8MiB live, 35.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
10.0ms	1.069365594933868e-35	1.9917849120412867e-33
14.0ms	-782293.9194829536	-14995.31996905418

Samples

13.0ms

224×

valid

Compiler

Compiled 431 to 321 computations (25.5% saved)

Precisions

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

ival-div: 3.0ms (40.2% of total)

ival-cosh: 3.0ms (40.2% of total)

ival-mult: 1.0ms (13.4% 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	-6.1133452891199524e-207	-9.278350499585363e-253

Compiler

Compiled 11 to 13 computations (-18.2% saved)

simplify4.0ms (0.3%)

Memory: 8.6MiB live, 8.6MiB allocated

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze73.0ms (5.2%)

sample980.0ms (70.2%)

explain81.0ms (5.8%)

preprocess3.0ms (0.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize25.0ms (1.8%)

series22.0ms (1.5%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune1.0ms (0.1%)

simplify0.0ms (0%)

localize35.0ms (2.5%)

series10.0ms (0.7%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune9.0ms (0.6%)

simplify0.0ms (0%)

localize20.0ms (1.4%)

series20.0ms (1.4%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune3.0ms (0.2%)

regimes21.0ms (1.5%)

regimes11.0ms (0.8%)

regimes13.0ms (0.9%)

regimes8.0ms (0.5%)

regimes8.0ms (0.6%)

bsearch0.0ms (0%)

bsearch16.0ms (1.1%)

bsearch26.0ms (1.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.3%)

end0.0ms (0%)

Profiling