Metrics for Numeric.SpecFunctions:logGammaCorrection from math-functions-0.1.5.2

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
100%	100%	0%	0%	0%	0%	0%	1

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample1.1s (58.9%)

Memory

39.1MiB live, 681.8MiB allocated; 175ms collecting garbage

Samples

846.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 617.0ms

ival-sub!: 514.0ms (83.3% of total)

ival-mult!: 101.0ms (16.4% of total)

adjust: 2.0ms (0.3% of total)

Bogosity

explain57.0ms (3.1%)

Memory

29.4MiB live, 76.1MiB allocated; 4ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
-	-	`#s(literal 2 binary64)`
-	-	`#s(literal 1 binary64)`
-	-	`(.f64 (.f64 x x) #s(literal 2 binary64))`
-	-	`(*.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

17.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult!: 5.0ms (79.6% of total)

ival-sub!: 1.0ms (15.9% of total)

adjust: 0.0ms (0% of total)

preprocess165.0ms (9%)

Memory

2.1MiB live, 104.0MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	29	22
2	83	22
3	237	22
4	757	21
5	3878	21
0	6	7
0	9	7
1	19	7
2	56	7
3	202	7
4	660	7
5	4036	7
0	8535	6

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

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

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune4.0ms (0.2%)

Memory

-43.4MiB live, 0.7MiB allocated; 6ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Compiler

Compiled 7 to 6 computations (14.3% saved)

series3.0ms (0.2%)

Memory

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

Counts

6 → 7

Calls

Call 1

Inputs
(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))
(.f64 (.f64 x x) #s(literal 2 binary64))
(*.f64 x x)
x
#s(literal 2 binary64)
#s(literal 1 binary64)

Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (* (* x x) 2) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (* x x) #s(hole binary64 (pow x 2)))
#s(approx x #s(hole binary64 x))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)
1.0ms	x	@	-inf	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)
1.0ms	x	@	0	((- (* (* x x) 2) 1) (* (* x x) 2) (* x x) x 2 1)

rewrite69.0ms (3.7%)

Memory

40.5MiB live, 86.2MiB allocated; 4ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	95
0	26	93
1	97	93
0	538	87

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

13 → 88

Calls

Call 1

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

Outputs
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64))) (neg.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)))
(/.f64 (fma.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64) #s(literal -1 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64))))
(fma.f64 (*.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x) #s(literal -1 binary64))
(fma.f64 (*.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x) #s(literal -1 binary64))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (*.f64 (neg.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)) #s(literal -1 binary64))
(fma.f64 (neg.f64 x) (neg.f64 x) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (fabs.f64 x) (*.f64 (fabs.f64 x) #s(literal 2 binary64)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (+.f64 (fabs.f64 x) (fabs.f64 x)) #s(literal -1 binary64))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 (*.f64 x x) #s(literal 2 binary64) #s(literal -1 binary64))
(fma.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 1 binary64) #s(literal -1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 #s(literal 2 binary64) (*.f64 x x) #s(literal -1 binary64))
(fma.f64 x (.f64 (.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64))
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
(fma.f64 x (*.f64 #s(literal 2 binary64) x) #s(literal -1 binary64))
(fma.f64 x x (-.f64 (*.f64 x x) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64)) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64))))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 8 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 2 binary64) #s(literal 1 binary64)) (pow.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64)))))
(-.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal 1 binary64))
(+.f64 (.f64 x x) (-.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (.f64 (.f64 #s(literal 2 binary64) x) x) #s(literal -1 binary64))
(.f64 (.f64 #s(literal 2 binary64) (neg.f64 x)) (neg.f64 x))
(.f64 (.f64 #s(literal 2 binary64) (fabs.f64 x)) (fabs.f64 x))
(.f64 (.f64 #s(literal 2 binary64) x) x)
(.f64 (neg.f64 x) (.f64 (neg.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 x) (+.f64 (neg.f64 x) (neg.f64 x)))
(.f64 (fabs.f64 x) (.f64 (fabs.f64 x) #s(literal 2 binary64)))
(*.f64 (fabs.f64 x) (+.f64 (fabs.f64 x) (fabs.f64 x)))
(.f64 (.f64 x x) #s(literal 2 binary64))
(.f64 (.f64 (*.f64 #s(literal 2 binary64) x) x) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 (*.f64 #s(literal 2 binary64) x) x))
(.f64 #s(literal 2 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(.f64 #s(literal 2 binary64) (.f64 x x))
(.f64 x (.f64 (*.f64 #s(literal 2 binary64) x) #s(literal 1 binary64)))
(*.f64 x (+.f64 x x))
(.f64 x (.f64 #s(literal 2 binary64) x))
(/.f64 (.f64 (.f64 (*.f64 #s(literal 2 binary64) x) x) #s(literal 2 binary64)) #s(literal 2 binary64))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (.f64 x x) (.f64 x x)))
(/.f64 (+.f64 (pow.f64 (.f64 x x) #s(literal 3 binary64)) (pow.f64 (.f64 x x) #s(literal 3 binary64))) (fma.f64 (.f64 x x) (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x)))))
(fma.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)) (*.f64 x x))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) (*.f64 x x))
(fma.f64 (neg.f64 x) (neg.f64 x) (*.f64 x x))
(fma.f64 (fabs.f64 x) (fabs.f64 x) (*.f64 x x))
(fma.f64 (.f64 x x) #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal 1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x x) (.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 x x (*.f64 x x))
(-.f64 (.f64 x x) (.f64 (neg.f64 x) x))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 #s(literal 1 binary64) (.f64 x x)))
(+.f64 (.f64 (.f64 x x) #s(literal 1 binary64)) (.f64 (.f64 x x) #s(literal 1 binary64)))
(+.f64 (.f64 x x) (.f64 x x))
(*.f64 (neg.f64 (neg.f64 x)) (neg.f64 (neg.f64 x)))
(*.f64 (neg.f64 (fabs.f64 x)) (neg.f64 (fabs.f64 x)))
(*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (fabs.f64 x)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (fabs.f64 x) (fabs.f64 x))
(*.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 (fabs.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))
(fabs.f64 (*.f64 x x))
(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))))
x
#s(literal 2 binary64)
#s(literal 1 binary64)
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) (fma.f64 (*.f64 #s(literal 2 binary64) x) x #s(literal -1 binary64)))
#s(approx (* (* x x) 2) (.f64 (.f64 #s(literal 2 binary64) x) x))
#s(approx (* x x) (*.f64 x x))
#s(approx x x)
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 #s(literal 2 binary64) x) x))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 (-.f64 #s(literal 2 binary64) (pow.f64 x #s(literal -2 binary64))) x) x))

eval146.0ms (8%)

Memory: -56.9MiB live, 18.6MiB allocated; 149ms collecting garbage
Compiler: Compiled 973 to 214 computations (78% saved)

prune3.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	2	91

Accuracy

100.0%

Counts

91 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
▶	48.8%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 15 to 12 computations (20% saved)

series2.0ms (0.1%)

Memory

1.8MiB live, 1.8MiB allocated; 0ms collecting garbage

Counts

5 → 10

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx x #s(hole binary64 x))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((- (* (* x x) 2) 1) -1 (+ (* x (+ x x)) -1) x (+ x x))
1.0ms	x	@	-inf	((- (* (* x x) 2) 1) -1 (+ (* x (+ x x)) -1) x (+ x x))
1.0ms	x	@	inf	((- (* (* x x) 2) 1) -1 (+ (* x (+ x x)) -1) x (+ x x))

rewrite97.0ms (5.3%)

Memory

-5.8MiB live, 48.7MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	138
0	30	138
1	126	45
0	973	45

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound
1×	iter limit

Counts

15 → 15

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(literal -1 binary64)
#s(literal 1 binary64)
x
#s(literal 2 binary64)
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
#s(approx x x)
#s(approx (+ x x) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 #s(literal 1 binary64) x) x))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 #s(literal 1 binary64) x) x))

eval1.0ms (0.1%)

Memory: 3.1MiB live, 3.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 110 to 27 computations (75.5% saved)

prune2.0ms (0.1%)

Memory

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

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	12	5	17

Accuracy

100.0%

Counts

17 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
▶	51.6%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
▶	2.9%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
▶	2.9%	#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
✓	48.8%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 41 to 34 computations (17.1% saved)

series2.0ms (0.1%)

Memory

4.1MiB live, 4.1MiB allocated; 0ms collecting garbage

Counts

8 → 10

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 -1))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 -1))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (- (* 2 (pow x 2)) 1)))
#s(approx x #s(hole binary64 x))
#s(approx (+ x x) #s(hole binary64 (* 2 x)))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (- (* (* x x) 2) 1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* 2 (pow x 2))))
#s(approx (+ (* x (+ x x)) -1) #s(hole binary64 (* (pow x 2) (- 2 (/ 1 (pow x 2))))))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((- (* (* x x) 2) 1) 1 (- (* (* x x) 2) 1) 2 (+ (* x (+ x x)) -1) x (+ x x) -1)
1.0ms	x	@	inf	((- (* (* x x) 2) 1) 1 (- (* (* x x) 2) 1) 2 (+ (* x (+ x x)) -1) x (+ x x) -1)
0.0ms	x	@	0	((- (* (* x x) 2) 1) 1 (- (* (* x x) 2) 1) 2 (+ (* x (+ x x)) -1) x (+ x x) -1)

Time

Variable

Point

Expression

1.0ms

-inf

((- (* (* x x) 2) 1) 1 (- (* (* x x) 2) 1) 2 (+ (* x (+ x x)) -1) x (+ x x) -1)

1.0ms

inf

((- (* (* x x) 2) 1) 1 (- (* (* x x) 2) 1) 2 (+ (* x (+ x x)) -1) x (+ x x) -1)

0.0ms

((- (* (* x x) 2) 1) 1 (- (* (* x x) 2) 1) 2 (+ (* x (+ x x)) -1) x (+ x x) -1)

rewrite57.0ms (3.1%)

Memory

-8.2MiB live, 36.4MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	157
0	33	131
1	141	57
0	1110	57

Stop Event

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

Counts

18 → 31

Calls

Call 1

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

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
#s(literal 1 binary64)
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64))) (-.f64 #s(literal -1 binary64) (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal -1 binary64))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64))) (neg.f64 (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x)) (pow.f64 (*.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal -1 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64)) (.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal -1 binary64)))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 3 binary64)) #s(literal -1 binary64)) (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x)) (pow.f64 (*.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64))))
(fma.f64 #s(approx (+ x x) #s(literal 2 binary64)) x #s(literal -1 binary64))
(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64)) (-.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal -1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal -1 binary64))))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 #s(approx (+ x x) #s(literal 2 binary64))) x))
(-.f64 #s(literal -1 binary64) (*.f64 (neg.f64 x) #s(approx (+ x x) #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x)) (pow.f64 (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (.f64 #s(approx (+ x x) #s(literal 2 binary64)) x)) (pow.f64 (*.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal 2 binary64)))))
(+.f64 (*.f64 #s(approx (+ x x) #s(literal 2 binary64)) x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (*.f64 #s(approx (+ x x) #s(literal 2 binary64)) x))
x
#s(approx (+ x x) #s(literal 2 binary64))
#s(literal -1 binary64)
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
#s(approx x x)
#s(approx (+ x x) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 1 binary64)))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
#s(approx (- (* (* x x) 2) 1) (.f64 (.f64 x x) #s(literal 1 binary64)))

eval2.0ms (0.1%)

Memory: 4.5MiB live, 4.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 402 to 58 computations (85.6% saved)

prune3.0ms (0.2%)

Memory

6.6MiB live, 6.6MiB allocated; 0ms collecting garbage

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	25	0	25
Fresh	0	0	0
Picked	0	3	3
Done	0	2	2
Total	25	5	30

Accuracy

100.0%

Counts

30 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
✓	51.6%	(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
✓	2.9%	#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))
✓	2.9%	#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
✓	48.8%	#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Compiler

Compiled 89 to 54 computations (39.3% saved)

regimes14.0ms (0.7%)

Memory

-24.3MiB live, 19.4MiB allocated; 5ms collecting garbage

Counts

6 → 1

Calls

Call 1

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

Outputs
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))

Calls

4 calls:

2.0ms	x
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	(*.f64 x x)
2.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.4%)

Memory

16.5MiB live, 16.5MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

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

Outputs
(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))

Calls

4 calls:

2.0ms	x
2.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
2.0ms	(*.f64 x x)
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
51.6%	1	`(*.f64 x x)`
51.6%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
51.6%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
51.6%	1	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes6.0ms (0.3%)

Memory

15.7MiB live, 15.7MiB allocated; 0ms collecting garbage

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 2 binary64))

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))
#s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64))

Calls

4 calls:

2.0ms	x
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(*.f64 x x)
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
50.5%	2	`(*.f64 x x)`
50.5%	2	`(.f64 (.f64 x x) #s(literal 2 binary64))`
50.5%	2	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
50.5%	2	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes4.0ms (0.2%)

Memory

10.8MiB live, 10.8MiB allocated; 0ms collecting garbage

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Outputs
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(.f64 (.f64 x x) #s(literal 2 binary64))
1.0ms	(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))

Results

Accuracy	Segments	Branch
48.8%	1	`(*.f64 x x)`
48.8%	1	`(.f64 (.f64 x x) #s(literal 2 binary64))`
48.8%	1	`(-.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) #s(literal 1 binary64))`
48.8%	1	`x`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch13.0ms (0.7%)

Memory

-44.5MiB live, 12.7MiB allocated; 6ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.49514041484229326	0.8642342797732173

Samples

2.0ms

64×

valid

Compiler

Compiled 82 to 82 computations (0% saved)

Precisions

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

ival-mult!: 1.0ms (134.3% of total)

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

adjust: 0.0ms (0% of total)

simplify45.0ms (2.5%)

Memory

3.1MiB live, 49.9MiB allocated; 3ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	45
1	28	45
2	64	45
3	220	45
4	1089	45
5	4443	45

Stop Event

1×	node limit

Calls

Call 1

Inputs
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(if (<=.f64 x #s(literal 3242591731706757/4503599627370496 binary64)) #s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64)) #s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64)))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

Outputs
(fma.f64 x (+.f64 x x) #s(literal -1 binary64))
(fma.f64 x #s(approx (+ x x) #s(literal 2 binary64)) #s(literal -1 binary64))
(if (<=.f64 x #s(literal 3242591731706757/4503599627370496 binary64)) #s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64)) #s(approx (- (* (* x x) 2) 1) #s(literal 1 binary64)))
#s(approx (- (* (* x x) 2) 1) #s(literal -1 binary64))

derivations16.0ms (0.9%)

Memory

14.0MiB live, 14.0MiB allocated; 0ms collecting garbage

Stop Event

1×

done

Compiler

Compiled 45 to 19 computations (57.8% saved)

preprocess32.0ms (1.7%)

Memory: -14.7MiB live, 31.1MiB allocated; 4ms collecting garbage
Remove: (abs x)
Compiler: Compiled 116 to 58 computations (50% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample1.1s (58.9%)

explain57.0ms (3.1%)

preprocess165.0ms (9%)

eval0.0ms (0%)

prune4.0ms (0.2%)

series3.0ms (0.2%)

rewrite69.0ms (3.7%)

eval146.0ms (8%)

prune3.0ms (0.1%)

series2.0ms (0.1%)

rewrite97.0ms (5.3%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

series2.0ms (0.1%)

rewrite57.0ms (3.1%)

eval2.0ms (0.1%)

prune3.0ms (0.2%)

regimes14.0ms (0.7%)

regimes7.0ms (0.4%)

regimes6.0ms (0.3%)

regimes4.0ms (0.2%)

bsearch13.0ms (0.7%)

simplify45.0ms (2.5%)

derivations16.0ms (0.9%)

preprocess32.0ms (1.7%)

end0.0ms (0%)

Profiling