Metrics for Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, F

start0.0ms (0%)

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

analyze93.0ms (3.7%)

Memory

-20.6MiB live, 122.8MiB allocated; 25ms collecting garbage

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
0%	0%	99.9%	0.1%	0%	0%	0%	4
6.7%	6.2%	87.4%	0.1%	0%	6.2%	0%	5
20.7%	18.7%	71.8%	0.1%	0%	9.4%	0%	6
34.5%	29.7%	56.2%	0.1%	0%	14%	0%	7
50.5%	42.1%	41.4%	0.1%	0%	16.4%	0%	8
61.4%	49.6%	31.2%	0.1%	0%	19.1%	0%	9
72.2%	57.4%	22%	0.1%	0%	20.5%	0%	10
79%	61.6%	16.4%	0.1%	0%	22%	0%	11
85.3%	65.9%	11.4%	0.1%	0%	22.7%	0%	12

Compiler

Compiled 13 to 10 computations (23.1% saved)

sample1.7s (69.3%)

Memory

25.0MiB live, 1 782.1MiB allocated; 266ms collecting garbage

Samples

1.1s	3 952×	1	valid
323.0ms	4 304×	0	valid
18.0ms	262×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-log: 565.0ms (49% of total)

ival-div: 209.0ms (18.1% of total)

adjust: 109.0ms (9.5% of total)

ival-exp: 96.0ms (8.3% of total)

ival-mult: 90.0ms (7.8% of total)

ival-add: 80.0ms (6.9% of total)

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

Bogosity

explain188.0ms (7.5%)

Memory

25.0MiB live, 213.5MiB allocated; 23ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
153	34	(4.171989712720398e+212 -1.390643191593077e-135)	2	(-3.7622869967926916e-253 -2.3985458606540134e+61)	`(log.f64 (/.f64 x (+.f64 x y)))`
36	0	-	3	(1.2233342712621701e+119 7.031750391210932e-204)	`(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))`
0	1	(8.991643929835807e+283 -554.4884810222419)	0	-	`(exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y)))))`
0	0	-	0	-	`y`
0	0	-	0	-	`(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)`
0	0	-	0	-	`(/.f64 x (+.f64 x y))`
0	0	-	0	-	`(+.f64 x y)`
0	0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (/.f64 x (+.f64 x y)))`	sensitivity	165	0
`*.f64`	`(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))`	*nu**	33	0
`log.f64`	`(log.f64 (/.f64 x (+.f64 x y)))`	uflow-rescue	20	0
↳	`(log.f64 (/.f64 x (+.f64 x y)))`	underflow	33
↳	`(/.f64 x (+.f64 x y))`	underflow	20
`exp.f64`	`(exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y)))))`	sensitivity	1	1

Confusion

	Predicted +	Predicted -
+	66	0
-	119	71

Precision

0.3567567567567568

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	66	0	0
-	119	0	71

Precision?

0.3567567567567568

Recall?

1.0

Freqs

test

number	freq
0	71
1	151
2	34

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

58.0ms	250×	1	valid
41.0ms	72×	2	valid
15.0ms	190×	0	valid

Compiler

Compiled 103 to 28 computations (72.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 91.0ms

ival-log: 50.0ms (54.8% of total)

ival-div: 13.0ms (14.3% of total)

adjust: 8.0ms (8.8% of total)

ival-exp: 7.0ms (7.7% of total)

ival-add: 6.0ms (6.6% of total)

ival-mult: 6.0ms (6.6% of total)

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

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

preprocess205.0ms (8.1%)

Memory

-18.7MiB live, 26.2MiB allocated; 8ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	78
1	74	64
2	168	62
3	463	62
4	1476	62
0	11	11
0	15	11
0	15	11

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)

Outputs
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)

Compiler

Compiled 11 to 8 computations (27.3% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	75.4%	(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)

Compiler

Compiled 11 to 8 computations (27.3% saved)

series27.0ms (1.1%)

Memory

-10.7MiB live, 34.4MiB allocated; 7ms collecting garbage

Counts

8 → 110

Calls

Call 1

Inputs
(/.f64 (exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y))))) x)
(exp.f64 (*.f64 x (log.f64 (/.f64 x (+.f64 x y)))))
(*.f64 x (log.f64 (/.f64 x (+.f64 x y))))
x
(log.f64 (/.f64 x (+.f64 x y)))
(/.f64 x (+.f64 x y))
(+.f64 x y)
y

Outputs
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ 1 x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (+ 1 (* x (+ (log x) (log (/ 1 y))))) x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (+ 1 (* x (+ (log x) (+ (log (/ 1 y)) (* x (- (* 1/2 (pow (+ (log x) (log (/ 1 y))) 2)) (/ 1 y))))))) x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (+ 1 (* x (+ (log x) (+ (log (/ 1 y)) (* x (- (+ (* 1/2 (pow (+ (log x) (log (/ 1 y))) 2)) (* x (+ (* -1 (/ (+ (log x) (log (/ 1 y))) y)) (+ (* 1/6 (pow (+ (log x) (log (/ 1 y))) 3)) (* 1/2 (/ 1 (pow y 2))))))) (/ 1 y))))))) x)))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 1))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ 1 (* x (+ (log x) (log (/ 1 y)))))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ 1 (* x (+ (log x) (+ (log (/ 1 y)) (* x (- (* 1/2 (pow (+ (log x) (log (/ 1 y))) 2)) (/ 1 y)))))))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ 1 (* x (+ (log x) (+ (log (/ 1 y)) (* x (- (+ (* 1/2 (pow (+ (log x) (log (/ 1 y))) 2)) (* x (+ (* -1 (/ (+ (log x) (log (/ 1 y))) y)) (+ (* 1/6 (pow (+ (log x) (log (/ 1 y))) 3)) (* 1/2 (/ 1 (pow y 2))))))) (/ 1 y)))))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* x (+ (log x) (log (/ 1 y))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* x (+ (log x) (+ (log (/ 1 y)) (* -1 (/ x y)))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* x (+ (log x) (+ (log (/ 1 y)) (* x (- (* 1/2 (/ x (pow y 2))) (/ 1 y))))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* x (+ (log x) (+ (log (/ 1 y)) (* x (- (* x (+ (* -1/3 (/ x (pow y 3))) (* 1/2 (/ 1 (pow y 2))))) (/ 1 y))))))))
#s(approx x #s(hole binary64 x))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log x) (log (/ 1 y)))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log x) (+ (log (/ 1 y)) (* -1 (/ x y))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log x) (+ (log (/ 1 y)) (* x (- (* 1/2 (/ x (pow y 2))) (/ 1 y)))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log x) (+ (log (/ 1 y)) (* x (- (* x (+ (* -1/3 (/ x (pow y 3))) (* 1/2 (/ 1 (pow y 2))))) (/ 1 y)))))))
#s(approx (/ x (+ x y)) #s(hole binary64 (/ x y)))
#s(approx (/ x (+ x y)) #s(hole binary64 (* x (+ (* -1 (/ x (pow y 2))) (/ 1 y)))))
#s(approx (/ x (+ x y)) #s(hole binary64 (* x (+ (* x (- (/ x (pow y 3)) (/ 1 (pow y 2)))) (/ 1 y)))))
#s(approx (/ x (+ x y)) #s(hole binary64 (* x (+ (* x (- (* x (+ (* -1 (/ x (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)))))
#s(approx (+ x y) #s(hole binary64 y))
#s(approx (+ x y) #s(hole binary64 (+ x y)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (exp (* -1 y)) x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (+ (exp (* -1 y)) (* 1/2 (/ (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) x))) x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (+ (exp (* -1 y)) (+ (* 1/2 (/ (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) x)) (/ (* (exp (* -1 y)) (+ (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2)) (* 1/6 (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3))))))) (pow x 2)))) x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (+ (exp (* -1 y)) (+ (* 1/2 (/ (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) x)) (+ (/ (* (exp (* -1 y)) (+ (* 1/48 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 3)) (+ (* 1/24 (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4)))))) (* 1/12 (* (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3)))) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))))))) (pow x 3)) (/ (* (exp (* -1 y)) (+ (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2)) (* 1/6 (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3))))))) (pow x 2))))) x)))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (exp (* -1 y))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* -1 y)) (* 1/2 (/ (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) x)))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* -1 y)) (+ (* 1/2 (/ (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) x)) (/ (* (exp (* -1 y)) (+ (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2)) (* 1/6 (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3))))))) (pow x 2))))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* -1 y)) (+ (* 1/2 (/ (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) x)) (+ (/ (* (exp (* -1 y)) (+ (* 1/48 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 3)) (+ (* 1/24 (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4)))))) (* 1/12 (* (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3)))) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))))))) (pow x 3)) (/ (* (exp (* -1 y)) (+ (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2)) (* 1/6 (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3))))))) (pow x 2)))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* -1 y)))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 y) (* 1/2 (/ (+ (* -1 (pow y 2)) (* 2 (pow y 2))) x)))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 y) (+ (* 1/6 (/ (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3)))) (pow x 2))) (* 1/2 (/ (+ (* -1 (pow y 2)) (* 2 (pow y 2))) x))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 y) (+ (* 1/24 (/ (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4))))) (pow x 3))) (+ (* 1/6 (/ (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3)))) (pow x 2))) (* 1/2 (/ (+ (* -1 (pow y 2)) (* 2 (pow y 2))) x)))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (* -1 (/ y x))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (/ (+ (* -1 y) (* 1/2 (/ (+ (* -1 (pow y 2)) (* 2 (pow y 2))) x))) x)))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (/ (+ (* -1 y) (+ (* 1/6 (/ (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3)))) (pow x 2))) (* 1/2 (/ (+ (* -1 (pow y 2)) (* 2 (pow y 2))) x)))) x)))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (/ (+ (* -1 y) (+ (* 1/24 (/ (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4))))) (pow x 3))) (+ (* 1/6 (/ (+ (* -6 (pow y 3)) (+ (* -2 (pow y 3)) (* 6 (pow y 3)))) (pow x 2))) (* 1/2 (/ (+ (* -1 (pow y 2)) (* 2 (pow y 2))) x))))) x)))
#s(approx (/ x (+ x y)) #s(hole binary64 1))
#s(approx (/ x (+ x y)) #s(hole binary64 (+ 1 (* -1 (/ y x)))))
#s(approx (/ x (+ x y)) #s(hole binary64 (- (+ 1 (/ (pow y 2) (pow x 2))) (/ y x))))
#s(approx (/ x (+ x y)) #s(hole binary64 (- (+ 1 (* -1 (/ (pow y 3) (pow x 3)))) (+ (* -1 (/ (pow y 2) (pow x 2))) (/ y x)))))
#s(approx (+ x y) #s(hole binary64 x))
#s(approx (+ x y) #s(hole binary64 (* x (+ 1 (/ y x)))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (* -1 (/ (+ (* -1 (exp (* -1 y))) (* -1/2 (/ (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) x))) x))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (* -1 (/ (+ (* -1 (exp (* -1 y))) (* -1 (/ (+ (* 1/2 (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2))))) (/ (* (exp (* -1 y)) (+ (* -1/6 (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3))))) (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2)))) x)) x))) x))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (* -1 (/ (+ (* -1 (exp (* -1 y))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (exp (* -1 y)) (+ (* -1/6 (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3))))) (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2))))) (/ (* (exp (* -1 y)) (+ (* -1/24 (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4)))))) (+ (* -1/48 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 3)) (* 1/12 (* (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3)))) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))))))) x)) x)) (* 1/2 (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))))) x))) x))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* -1 y)) (* -1 (/ (+ (* -1 (/ (* (exp (* -1 y)) (+ (* -1/6 (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3))))) (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2)))) x)) (* -1/2 (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))))) x)))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* -1 y)) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* -1 y)) (+ (* -1/24 (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4)))))) (+ (* -1/48 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 3)) (* 1/12 (* (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3)))) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))))))) x)) (* (exp (* -1 y)) (+ (* -1/6 (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3))))) (* 1/8 (pow (+ (* -1 (pow y 2)) (* 2 (pow y 2))) 2))))) x)) (* -1/2 (* (exp (* -1 y)) (+ (* -1 (pow y 2)) (* 2 (pow y 2)))))) x)))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 y) (* -1 (/ (+ (* -1/2 (+ (* -1 (pow y 2)) (* 2 (pow y 2)))) (* 1/6 (/ (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3)))) x))) x)))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3))))) (* 1/24 (/ (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4))))) x))) x)) (* -1/2 (+ (* -1 (pow y 2)) (* 2 (pow y 2))))) x)))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (* -1 (/ (+ y (* -1/2 (/ (+ (* -1 (pow y 2)) (* 2 (pow y 2))) x))) x))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (* -1 (/ (+ y (* -1 (/ (+ (* -1/6 (/ (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3)))) x)) (* 1/2 (+ (* -1 (pow y 2)) (* 2 (pow y 2))))) x))) x))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (* -1 (/ (+ y (* -1 (/ (+ (* -1 (/ (+ (* -1/24 (/ (+ (* -24 (pow y 4)) (+ (* -12 (pow y 4)) (+ (* -6 (pow y 4)) (* 48 (pow y 4))))) x)) (* 1/6 (+ (* -6 (pow y 3)) (+ (* 2 (pow y 3)) (* 6 (pow y 3)))))) x)) (* 1/2 (+ (* -1 (pow y 2)) (* 2 (pow y 2))))) x))) x))))
#s(approx (/ x (+ x y)) #s(hole binary64 (+ 1 (* -1 (/ (- (* -1 (/ (pow y 2) x)) (* -1 y)) x)))))
#s(approx (/ x (+ x y)) #s(hole binary64 (+ 1 (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow y 3) x)) (* -1 (pow y 2))) x)) (* -1 y)) x)))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* x (- (* -1 (/ y x)) 1)))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* -1 (/ y x)) (/ 1 x))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* y (- (* y (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))) (/ 1 x))) (/ 1 x))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* y (- (* y (+ (* -1 (/ (* y (+ 1/6 (+ (* 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))) x)) (+ (* 1/2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2)))))) (/ 1 x))) (/ 1 x))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ 1 (* -1 y))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ 1 (* y (- (* y (+ 1/2 (* 1/2 (/ 1 x)))) 1)))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ 1 (* y (- (* y (+ 1/2 (+ (* -1 (* y (+ 1/6 (+ (* 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x)))))) (* 1/2 (/ 1 x))))) 1)))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* y (- (* 1/2 (/ y x)) 1))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* y (- (* y (+ (* -1/3 (/ y (pow x 2))) (* 1/2 (/ 1 x)))) 1))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* y (- (* y (+ (* y (- (* 1/4 (/ y (pow x 3))) (* 1/3 (/ 1 (pow x 2))))) (* 1/2 (/ 1 x)))) 1))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (* y (- (* 1/2 (/ y (pow x 2))) (/ 1 x)))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (* y (- (* y (+ (* -1/3 (/ y (pow x 3))) (* 1/2 (/ 1 (pow x 2))))) (/ 1 x)))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (* y (- (* y (+ (* y (- (* 1/4 (/ y (pow x 4))) (* 1/3 (/ 1 (pow x 3))))) (* 1/2 (/ 1 (pow x 2))))) (/ 1 x)))))
#s(approx (/ x (+ x y)) #s(hole binary64 (+ 1 (* y (- (/ y (pow x 2)) (/ 1 x))))))
#s(approx (/ x (+ x y)) #s(hole binary64 (+ 1 (* y (- (* y (+ (* -1 (/ y (pow x 3))) (/ 1 (pow x 2)))) (/ 1 x))))))
#s(approx y #s(hole binary64 y))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (exp (* x (+ (log x) (log (/ 1 y))))) x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* -1 (/ (* x (exp (* x (+ (log x) (log (/ 1 y)))))) y)) (/ (exp (* x (+ (log x) (log (/ 1 y))))) x))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* -1 (/ (* x (exp (* x (+ (log x) (log (/ 1 y)))))) y)) (+ (/ (exp (* x (+ (log x) (log (/ 1 y))))) x) (/ (* (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4)))) (* x (pow y 2)))))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* -1 (/ (* x (exp (* x (+ (log x) (log (/ 1 y)))))) y)) (+ (/ (exp (* x (+ (log x) (log (/ 1 y))))) x) (+ (/ (* (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* -1/2 (* (pow x 3) (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (+ (* -1/6 (pow x 6)) (* 1/6 (* x (+ (* -6 (pow x 3)) (+ (* -2 (pow x 3)) (* 6 (pow x 3))))))))) (* x (pow y 3))) (/ (* (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4)))) (* x (pow y 2))))))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (exp (* x (+ (log x) (log (/ 1 y)))))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* x (+ (log x) (log (/ 1 y))))) (* -1 (/ (* (pow x 2) (exp (* x (+ (log x) (log (/ 1 y)))))) y)))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* -1 (/ (* (pow x 2) (exp (* x (+ (log x) (log (/ 1 y)))))) y)) (/ (* (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4)))) (pow y 2))))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* -1 (/ (* (pow x 2) (exp (* x (+ (log x) (log (/ 1 y)))))) y)) (+ (/ (* (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* -1/2 (* (pow x 3) (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (+ (* -1/6 (pow x 6)) (* 1/6 (* x (+ (* -6 (pow x 3)) (+ (* -2 (pow x 3)) (* 6 (pow x 3))))))))) (pow y 3)) (/ (* (exp (* x (+ (log x) (log (/ 1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4)))) (pow y 2)))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 (/ (pow x 2) y)) (* x (+ (log x) (log (/ 1 y)))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 (/ (pow x 2) y)) (+ (* 1/2 (/ (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2)))) (pow y 2))) (* x (+ (log x) (log (/ 1 y))))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 (/ (pow x 2) y)) (+ (* 1/6 (/ (* x (+ (* -6 (pow x 3)) (+ (* -2 (pow x 3)) (* 6 (pow x 3))))) (pow y 3))) (+ (* 1/2 (/ (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2)))) (pow y 2))) (* x (+ (log x) (log (/ 1 y)))))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log x) (+ (log (/ 1 y)) (+ (* -1 (/ x y)) (* 1/2 (/ (+ (* -1 (pow x 2)) (* 2 (pow x 2))) (pow y 2))))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log x) (+ (log (/ 1 y)) (+ (* -1 (/ x y)) (+ (* 1/6 (/ (+ (* -6 (pow x 3)) (+ (* -2 (pow x 3)) (* 6 (pow x 3)))) (pow y 3))) (* 1/2 (/ (+ (* -1 (pow x 2)) (* 2 (pow x 2))) (pow y 2)))))))))
#s(approx (/ x (+ x y)) #s(hole binary64 (/ (+ x (* -1 (/ (pow x 2) y))) y)))
#s(approx (/ x (+ x y)) #s(hole binary64 (/ (- (+ x (/ (pow x 3) (pow y 2))) (/ (pow x 2) y)) y)))
#s(approx (/ x (+ x y)) #s(hole binary64 (/ (- (+ x (* -1 (/ (pow x 4) (pow y 3)))) (+ (* -1 (/ (pow x 3) (pow y 2))) (/ (pow x 2) y))) y)))
#s(approx (+ x y) #s(hole binary64 (* y (+ 1 (/ x y)))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (/ (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) x)))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* -1 (/ (* x (exp (* x (+ (log (* -1 x)) (log (/ -1 y)))))) y)) (/ (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) x))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* -1 (/ (+ (* -1 (/ (* (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4)))) (* x y))) (* x (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))))) y)) (/ (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) x))))
#s(approx (/ (exp (* x (log (/ x (+ x y))))) x) #s(hole binary64 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (+ (* 1/6 (* x (+ (* -6 (pow x 3)) (+ (* 2 (pow x 3)) (* 6 (pow x 3)))))) (+ (* 1/6 (pow x 6)) (* 1/2 (* (pow x 3) (+ (* -1 (pow x 2)) (* 2 (pow x 2)))))))) (* x y))) (/ (* (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4)))) x)) y)) (* x (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))))) y)) (/ (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) x))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (exp (* x (+ (log (* -1 x)) (log (/ -1 y)))))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (* -1 (/ (* (pow x 2) (exp (* x (+ (log (* -1 x)) (log (/ -1 y)))))) y)))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (* -1 (/ (+ (* -1 (/ (* (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4)))) y)) (* (pow x 2) (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))))) y)))))
#s(approx (exp (* x (log (/ x (+ x y))))) #s(hole binary64 (+ (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (* (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (+ (* 1/6 (* x (+ (* -6 (pow x 3)) (+ (* 2 (pow x 3)) (* 6 (pow x 3)))))) (+ (* 1/6 (pow x 6)) (* 1/2 (* (pow x 3) (+ (* -1 (pow x 2)) (* 2 (pow x 2)))))))) y)) (* (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))) (+ (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) (* 1/2 (pow x 4))))) y)) (* (pow x 2) (exp (* x (+ (log (* -1 x)) (log (/ -1 y))))))) y)))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (* x (+ (log (* -1 x)) (log (/ -1 y))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 (/ (pow x 2) y)) (* x (+ (log (* -1 x)) (log (/ -1 y)))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 (/ (+ (* -1/2 (/ (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2)))) y)) (pow x 2)) y)) (* x (+ (log (* -1 x)) (log (/ -1 y)))))))
#s(approx (* x (log (/ x (+ x y)))) #s(hole binary64 (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/6 (/ (* x (+ (* -6 (pow x 3)) (+ (* 2 (pow x 3)) (* 6 (pow x 3))))) y)) (* 1/2 (* x (+ (* -1 (pow x 2)) (* 2 (pow x 2)))))) y)) (pow x 2)) y)) (* x (+ (log (* -1 x)) (log (/ -1 y)))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log (* -1 x)) (log (/ -1 y)))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log (* -1 x)) (+ (log (/ -1 y)) (* -1 (/ x y))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log (* -1 x)) (+ (log (/ -1 y)) (* -1 (/ (+ x (* -1/2 (/ (+ (* -1 (pow x 2)) (* 2 (pow x 2))) y))) y))))))
#s(approx (log (/ x (+ x y))) #s(hole binary64 (+ (log (* -1 x)) (+ (log (/ -1 y)) (* -1 (/ (+ x (* -1 (/ (+ (* -1/6 (/ (+ (* -6 (pow x 3)) (+ (* 2 (pow x 3)) (* 6 (pow x 3)))) y)) (* 1/2 (+ (* -1 (pow x 2)) (* 2 (pow x 2))))) y))) y))))))
#s(approx (/ x (+ x y)) #s(hole binary64 (* -1 (/ (+ (* -1 x) (/ (pow x 2) y)) y))))
#s(approx (/ x (+ x y)) #s(hole binary64 (* -1 (/ (+ (* -1 x) (* -1 (/ (- (/ (pow x 3) y) (pow x 2)) y))) y))))
#s(approx (/ x (+ x y)) #s(hole binary64 (* -1 (/ (+ (* -1 x) (* -1 (/ (- (* -1 (/ (- (/ (pow x 4) y) (pow x 3)) y)) (pow x 2)) y))) y))))
#s(approx (+ x y) #s(hole binary64 (* -1 (* y (- (* -1 (/ x y)) 1)))))

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ (exp (* x (log (/ x (+ x y))))) x) (exp (* x (log (/ x (+ x y))))) (* x (log (/ x (+ x y)))) x (log (/ x (+ x y))) (/ x (+ x y)) (+ x y) y)
4.0ms	x	@	inf	((/ (exp (* x (log (/ x (+ x y))))) x) (exp (* x (log (/ x (+ x y))))) (* x (log (/ x (+ x y)))) x (log (/ x (+ x y))) (/ x (+ x y)) (+ x y) y)
4.0ms	y	@	inf	((/ (exp (* x (log (/ x (+ x y))))) x) (exp (* x (log (/ x (+ x y))))) (* x (log (/ x (+ x y)))) x (log (/ x (+ x y))) (/ x (+ x y)) (+ x y) y)
3.0ms	y	@	0	((/ (exp (* x (log (/ x (+ x y))))) x) (exp (* x (log (/ x (+ x y))))) (* x (log (/ x (+ x y)))) x (log (/ x (+ x y))) (/ x (+ x y)) (+ x y) y)
3.0ms	y	@	-inf	((/ (exp (* x (log (/ x (+ x y))))) x) (exp (* x (log (/ x (+ x y))))) (* x (log (/ x (+ x y)))) x (log (/ x (+ x y))) (/ x (+ x y)) (+ x y) y)

rewrite260.0ms (10.3%)

Memory

16.2MiB live, 107.2MiB allocated; 37ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	796	5148
1	1018	5146
2	1019	5146
3	1020	5146
4	1021	5146
5	1022	5146
6	1023	5146
7	1024	5146
0	1024	5146
0	1024	5144
1	1235	5144
2	1417	5144
3	1579	5144
4	1730	5144
5	1859	5144
6	1966	5144
7	2030	5144
8	2072	5144
9	2100	5144
10	2116	5144
11	2121	5144
12	2122	5144

Stop Event

1×	saturated
1×	node limit
1×	saturated

end0.0ms (0%)

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

start0.0ms (0%)

analyze93.0ms (3.7%)

sample1.7s (69.3%)

explain188.0ms (7.5%)

preprocess205.0ms (8.1%)

eval0.0ms (0%)

prune0.0ms (0%)

series27.0ms (1.1%)

rewrite260.0ms (10.3%)

end0.0ms (0%)

Profiling