Metrics for cos2 (problem 3.4.1)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0.1%)

Memory

1.3MiB live, 1.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 10 to 8 computations (20% saved)

sample1.5s (77.4%)

Memory

65.5MiB live, 1 133.3MiB allocated

Samples

596.0ms	2 264×	2	valid
323.0ms	4 157×	0	valid
198.0ms	577×	3	valid
132.0ms	1 258×	1	valid

Precisions

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

ival-cos: 684.0ms (65.7% of total)

ival-div: 99.0ms (9.5% of total)

adjust: 97.0ms (9.3% of total)

ival-sub: 84.0ms (8.1% of total)

ival-mult: 61.0ms (5.9% of total)

ival-true: 6.0ms (0.6% of total)

exact: 5.0ms (0.5% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain129.0ms (6.6%)

Memory

-8.6MiB live, 112.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
72	1	(1.0062900105500921e+36)	1	(-8.260084990238072e+145)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
61	2	(-2.7727536760449067e+161)	2	(-3.6646562051866966e-156)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`
0	0	-	0	-	`(*.f64 x x)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	cancellation	72	2
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	u/u	54	0
↳	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`	underflow	54
↳	`(*.f64 x x)`	underflow	54
`/.f64`	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`	n/o	7	0
↳	`(*.f64 x x)`	overflow	69

Confusion

	Predicted +	Predicted -
+	128	1
-	5	122

Precision

0.9624060150375939

Recall

0.9922480620155039

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	128	1	0
-	5	1	121

Precision?

0.9555555555555556

Recall?

1.0

Freqs

test

number	freq
0	123
1	133

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

33.0ms	124×	2	valid
29.0ms	270×	0	valid
11.0ms	34×	3	valid
9.0ms	84×	1	valid

Compiler

Compiled 69 to 28 computations (59.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 66.0ms

ival-cos: 45.0ms (68.5% of total)

adjust: 6.0ms (9.1% of total)

ival-div: 5.0ms (7.6% of total)

ival-sub: 5.0ms (7.6% of total)

ival-mult: 4.0ms (6.1% of total)

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

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

exact: 0.0ms (0% of total)

preprocess2.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

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

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

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.1%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Calls

Call 1

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

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

localize46.0ms (2.3%)

Memory

-1.2MiB live, 36.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.0	(cos.f64 x)
accuracy	14.035061389727238	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
accuracy	15.725532592442665	(-.f64 #s(literal 1 binary64) (cos.f64 x))

Samples

16.0ms	62×	2	valid
10.0ms	135×	0	valid
8.0ms	17×	3	valid
4.0ms	42×	1	valid

Compiler

Compiled 40 to 14 computations (65% saved)

Precisions

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

ival-cos: 21.0ms (68.1% of total)

ival-div: 3.0ms (9.7% of total)

adjust: 3.0ms (9.7% of total)

ival-mult: 2.0ms (6.5% of total)

ival-sub: 2.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

4 → 16

Calls

Call 1

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

Outputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(- 1 (cos x))
(cos x)

Calls

3 calls:

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

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Counts

16 → 4

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(/ (- 1 (cos x)) (pow x 2))
(- 1 (cos x))
(cos x)

Outputs
1/2
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(+ 1/2 (* -1/24 (pow x 2)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(cos.f64 x)
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(*.f64 x x)

rewrite0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

4 → 4

Calls

Call 1

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

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

eval1.0ms (0%)

Memory: 1.1MiB live, 1.1MiB allocated
Compiler: Compiled 85 to 15 computations (82.4% saved)

prune2.0ms (0.1%)

Memory

2.2MiB live, 2.2MiB 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

60.2%

Counts

9 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.1%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
▶	3.6%	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
▶	3.3%	#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))
▶	10.7%	#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Calls

Call 1

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

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

localize48.0ms (2.5%)

Memory

1.7MiB live, 39.6MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(cos.f64 x)
accuracy	15.725532592442665	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	61.388251516586145	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
accuracy	0.0	(*.f64 x x)
accuracy	61.911408015743696	#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))
accuracy	0.0	(cos.f64 x)
accuracy	57.1587659210607	#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))

Samples

19.0ms	62×	2	valid
11.0ms	135×	0	valid
6.0ms	17×	3	valid
5.0ms	42×	1	valid

Compiler

Compiled 92 to 21 computations (77.2% saved)

Precisions

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

ival-cos: 20.0ms (65.7% of total)

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

adjust: 3.0ms (9.9% of total)

ival-mult: 2.0ms (6.6% of total)

ival-sub: 2.0ms (6.6% of total)

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

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

exact: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated

Counts

6 → 16

Calls

Call 1

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

Outputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (- 1 (cos x)) (pow x 2))
(cos x)
(- 1 (cos x))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((/ (- 1 (cos x)) (* x x)) (cos x) (/ (- 1 (cos x)) (* x x)) (* x x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)))
1.0ms	x	@	-inf	((/ (- 1 (cos x)) (* x x)) (cos x) (/ (- 1 (cos x)) (* x x)) (* x x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)))
0.0ms	x	@	0	((/ (- 1 (cos x)) (* x x)) (cos x) (/ (- 1 (cos x)) (* x x)) (* x x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)))

Time

Variable

Point

Expression

1.0ms

inf

((/ (- 1 (cos x)) (* x x)) (cos x) (/ (- 1 (cos x)) (* x x)) (* x x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)))

1.0ms

-inf

((/ (- 1 (cos x)) (* x x)) (cos x) (/ (- 1 (cos x)) (* x x)) (* x x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)))

0.0ms

((/ (- 1 (cos x)) (* x x)) (cos x) (/ (- 1 (cos x)) (* x x)) (* x x) (/ (- 1 (cos x)) (* x x)) (- 1 (cos x)))

simplify0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	egg-herbie

Counts

16 → 6

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(pow x 2)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (- 1 (cos x)) (pow x 2))
(cos x)
(- 1 (cos x))

Outputs
1/2
#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))
(+ 1/2 (* -1/24 (pow x 2)))
(cos.f64 x)
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(*.f64 x x)
1
#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(+ 1 (* -1/2 (pow x 2)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))

rewrite0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Counts

6 → 6

Calls

Call 1

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

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

eval1.0ms (0.1%)

Memory: 2.0MiB live, 2.0MiB allocated
Compiler: Compiled 212 to 23 computations (89.2% saved)

prune57.0ms (2.9%)

Memory

-54.8MiB live, 3.4MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	0	0	0
Picked	0	3	3
Done	0	1	1
Total	12	5	17

Accuracy

60.2%

Counts

17 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.1%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	3.6%	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
▶	10.7%	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	3.3%	#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))
✓	10.7%	#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))

Compiler

Compiled 62 to 44 computations (29% 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 #s(literal 1 binary64) (cos.f64 x))
cost-diff	0	#s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
cost-diff	0	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
cost-diff	0	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))

Calls

Call 1

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

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

localize46.0ms (2.3%)

Memory

9.8MiB live, 46.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	15.725532592442665	(-.f64 #s(literal 1 binary64) (cos.f64 x))
accuracy	15.725532592442665	(-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
accuracy	59.54925496934346	#s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
accuracy	61.388251516586145	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))

Samples

17.0ms	62×	2	valid
11.0ms	135×	0	valid
6.0ms	17×	3	valid
5.0ms	42×	1	valid

Compiler

Compiled 66 to 20 computations (69.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-cos: 19.0ms (66.5% of total)

ival-div: 3.0ms (10.5% of total)

adjust: 3.0ms (10.5% of total)

ival-mult: 2.0ms (7% of total)

ival-sub: 2.0ms (7% of total)

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

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

exact: 0.0ms (0% of total)

series1.0ms (0.1%)

Memory

2.5MiB live, 2.5MiB allocated

Counts

4 → 15

Calls

Call 1

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

Outputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(/ (- 1 (cos x)) (pow x 2))
(- 1 (cos x))
(cos x)

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (- 1 (cos x)))
0.0ms	x	@	-inf	((/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (- 1 (cos x)))
0.0ms	x	@	0	((/ (- 1 (cos x)) (* x x)) (- 1 (cos x)) (cos x) (- 1 (cos x)))

simplify0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	egg-herbie

Counts

15 → 4

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(/ (- 1 (cos x)) (pow x 2))
(- 1 (cos x))
(cos x)

Outputs
1/2
#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(+ 1/2 (* -1/24 (pow x 2)))
(-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
#s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(-.f64 #s(literal 1 binary64) (cos.f64 x))

rewrite0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Counts

4 → 4

Calls

Call 1

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

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

eval1.0ms (0%)

Memory: 1.3MiB live, 1.3MiB allocated
Compiler: Compiled 128 to 15 computations (88.3% saved)

prune3.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	7	0	7
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	7	5	12

Accuracy

60.2%

Counts

12 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	52.1%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
✓	3.6%	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	10.7%	#s(approx (/ (- 1 (cos x)) (* x x)) (-.f64 #s(literal 1 binary64) #s(approx (cos x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	3.3%	#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))
✓	10.7%	#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))

Compiler

Compiled 124 to 61 computations (50.8% saved)

regimes5.0ms (0.2%)

Memory

7.9MiB live, 7.9MiB allocated

Counts

5 → 3

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
60.2%	3	`x`
56.1%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes4.0ms (0.2%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
10.7%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
10.7%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

regimes2.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))

Outputs
#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
3.3%	1	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
3.3%	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

bsearch53.0ms (2.7%)

Memory

-19.6MiB live, 53.1MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
26.0ms	4.800512491520526e-16	78426720298.13364
23.0ms	-0.0013672554816697524	-5.96336074578724e-9

Samples

30.0ms	288×	1	valid
2.0ms	32×	0	valid

Compiler

Compiled 391 to 330 computations (15.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-sub: 8.0ms (33.8% of total)

ival-cos: 6.0ms (25.4% of total)

adjust: 4.0ms (16.9% of total)

ival-div: 3.0ms (12.7% of total)

ival-mult: 2.0ms (8.5% of total)

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

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

exact: 0.0ms (0% of total)

simplify5.0ms (0.2%)

Memory

8.2MiB live, 8.3MiB allocated

Algorithm

1×	egg-herbie

Calls

Call 1

Inputs

(if (<=.f64 x #s(literal -6346860552976803/604462909807314587353088 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x #s(literal 6346860552976803/604462909807314587353088 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))))

#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))

#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))

Outputs

(if (<=.f64 x #s(literal -6346860552976803/604462909807314587353088 binary64)) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)) (if (<=.f64 x #s(literal 6346860552976803/604462909807314587353088 binary64)) #s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x)) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))))

#s(approx (/ (- 1 (cos x)) (* x x)) (cos.f64 x))

#s(approx (/ (- 1 (cos x)) (* x x)) (*.f64 x x))

soundness1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Stop Event

1×

done

Compiler

Compiled 58 to 19 computations (67.2% saved)

preprocess26.0ms (1.3%)

Memory: -14.1MiB live, 30.7MiB allocated
Compiler: Compiled 132 to 50 computations (62.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0.1%)

sample1.5s (77.4%)

explain129.0ms (6.6%)

preprocess2.0ms (0.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

localize46.0ms (2.3%)

series3.0ms (0.1%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0%)

prune2.0ms (0.1%)

simplify0.0ms (0%)

localize48.0ms (2.5%)

series2.0ms (0.1%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0.1%)

prune57.0ms (2.9%)

simplify0.0ms (0%)

localize46.0ms (2.3%)

series1.0ms (0.1%)

simplify0.0ms (0%)

rewrite0.0ms (0%)

eval1.0ms (0%)

prune3.0ms (0.1%)

regimes5.0ms (0.2%)

regimes4.0ms (0.2%)

regimes2.0ms (0.1%)

bsearch53.0ms (2.7%)

simplify5.0ms (0.2%)

soundness1.0ms (0%)

preprocess26.0ms (1.3%)

end0.0ms (0%)

Profiling