Metrics for Logistic regression 2

analyze71.0ms (0.8%)

Memory

5.0MiB live, 79.5MiB 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
50%	50%	50%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
75%	74.9%	25%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
75%	74.9%	25%	0.1%	0%	0%	0%	7
75%	74.9%	25%	0.1%	0%	0%	0%	8
75%	74.9%	25%	0.1%	0%	0%	0%	9
75%	74.9%	25%	0.1%	0%	0%	0%	10
75%	74.9%	25%	0.1%	0%	0%	0%	11
75%	74.9%	25%	0.1%	0%	0%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.0s (12.1%)

Memory

33.3MiB live, 1 045.5MiB allocated

Samples

449.0ms	8 256×	0	valid
202.0ms	2 645×	1	exit

Precisions

Click to see histograms. Total time spent on operations: 383.0ms

ival-log1p: 115.0ms (30% of total)

ival-exp: 85.0ms (22.2% of total)

ival-mult: 80.0ms (20.9% of total)

ival-sub: 50.0ms (13.1% of total)

adjust: 40.0ms (10.4% of total)

ival-true: 8.0ms (2.1% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

preprocess34.0ms (0.4%)

Memory

-10.9MiB live, 26.7MiB allocated

Algorithm

1×	egg-herbie

Rules

148×	`lower-fma.f64`
148×	`lower-fma.f32`
108×	`lower-*.f32`
106×	`lower-*.f64`
78×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	51
1	58	49
2	113	49
3	227	49
4	311	49
5	429	49
6	483	49
7	515	49
8	518	49
0	8	9
0	13	9
1	22	9
2	33	9
3	45	9
4	60	9
5	84	9
6	123	9
7	160	9
8	205	9
9	231	9
10	255	9
11	264	9
0	264	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Outputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

explain105.0ms (1.3%)

Memory

-16.0MiB live, 110.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
1	90	(-8.008229979008722e+105 -5.839617628016665e-218)	-	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`
0	0	-	-	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
0	0	-	-	`(+.f64 #s(literal 1 binary64) (exp.f64 x))`
0	0	-	-	`y`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`(*.f64 x y)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`	sensitivity	90	0
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`	oflow-rescue	1	0
↳	`(exp.f64 x)`	overflow	1
↳	`(+.f64 #s(literal 1 binary64) (exp.f64 x))`	overflow	1

Confusion

	Predicted +	Predicted -
+	1	0
-	90	165

Precision

0.01098901098901099

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	90	0	165

Precision?

0.01098901098901099

Recall?

1.0

Freqs

test

number	freq
0	165
1	91

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 36 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-log1p: 5.0ms (25.7% of total)

ival-mult: 5.0ms (25.7% of total)

ival-exp: 4.0ms (20.6% of total)

ival-sub: 2.0ms (10.3% of total)

ival-add: 2.0ms (10.3% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify13.0ms (0.2%)

Memory

12.0MiB live, 12.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(exp.f64 x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	cost-diff	0	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
✓	cost-diff	192	(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Rules

148×	`lower-fma.f64`
148×	`lower-fma.f32`
108×	`lower-*.f32`
106×	`lower-*.f64`
52×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
0	13	26
1	22	26
2	33	26
3	45	26
4	60	26
5	84	26
6	123	26
7	160	26
8	205	26
9	231	26
10	255	26
11	264	26
0	264	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
#s(literal 1 binary64)
(exp.f64 x)
x
(*.f64 x y)
y

Outputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
#s(literal 1 binary64)
(exp.f64 x)
x
(*.f64 x y)
y

localize27.0ms (0.3%)

Memory

-11.1MiB live, 27.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (exp.f64 x))
✓	accuracy	100.0%	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
✓	accuracy	99.6%	(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Samples

16.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

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

ival-log1p: 3.0ms (33.7% of total)

ival-exp: 2.0ms (22.5% of total)

ival-mult: 2.0ms (22.5% of total)

ival-sub: 1.0ms (11.2% of total)

ival-add: 1.0ms (11.2% of total)

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

exact: 0.0ms (0% of total)

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

series55.0ms (0.7%)

Memory

31.5MiB live, 67.2MiB allocated

Counts

4 → 60

Calls

Call 1

Inputs
#<alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))>
#<alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))>
#<alt (+.f64 #s(literal 1 binary64) (exp.f64 x))>
#<alt (exp.f64 x)>

Outputs
#<alt (log 2)>
#<alt (+ (log 2) (* 1/2 x))>
#<alt (+ (log 2) (* x (+ 1/2 (* 1/8 x))))>
#<alt (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>
#<alt (exp x)>

Calls

15 calls:

Time	Variable		Point	Expression
30.0ms	x	@	inf	(log (+ 1 (exp x)))
20.0ms	x	@	-inf	(log (+ 1 (exp x)))
3.0ms	y	@	0	(- (log (+ 1 (exp x))) (* x y))
0.0ms	x	@	0	(log (+ 1 (exp x)))
0.0ms	x	@	inf	(- (log (+ 1 (exp x))) (* x y))

simplify261.0ms (3.1%)

Memory

1.6MiB live, 276.5MiB allocated

Algorithm

1×	egg-herbie

Rules

11 474×	`lower-fma.f64`
11 474×	`lower-fma.f32`
2 426×	`lower-*.f64`
2 426×	`lower-*.f32`
1 772×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	400
1	180	400
2	389	400
3	1353	400
4	4014	370
5	6856	370
0	8132	300

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

Inputs
(log 2)
(+ (log 2) (* 1/2 x))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 1/2 x))))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)
(exp x)

Outputs
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* x (- 1/2 y)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(fma.f64 x (fma.f64 x (fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal 1/8 binary64)) (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64)))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
2
#s(literal 2 binary64)
(+ 2 x)
(+.f64 #s(literal 2 binary64) x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 2 binary64))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+ 1 (exp x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* 1/2 x))))
(fma.f64 x (fma.f64 #s(literal 1/2 binary64) x #s(literal 1 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(fma.f64 x (fma.f64 x (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)
(exp x)
(exp.f64 x)

rewrite413.0ms (5%)

Memory

8.8MiB live, 397.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 436×	`lower-/.f64`
4 436×	`lower-/.f32`
3 924×	`lower-*.f32`
3 922×	`lower-*.f64`
3 690×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	20
0	13	20
1	47	20
2	311	20
3	2718	20
0	9051	16

Stop Event

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

Counts

4 → 359

Calls

Call 1

Inputs
(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(exp.f64 x)

Outputs
(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (log1p.f64 (exp.f64 x)) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (log1p.f64 (exp.f64 x)))
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(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) #s(literal -1 binary64)))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 3 binary64)))) (fma.f64 (.f64 (exp.f64 x) (expm1.f64 x)) (-.f64 (*.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64)))) (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (exp.f64 x) (expm1.f64 x)) #s(literal 2 binary64)))) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) (expm1.f64 x))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 9 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (-.f64 (exp.f64 (.f64 x #s(literal 6 binary64))) (exp.f64 (.f64 x #s(literal 3 binary64)))))))
(.f64 (pow.f64 (/.f64 (-.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 6 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (exp.f64 (*.f64 x #s(literal 4 binary64)))))))
(.f64 (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 4 binary64))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(exp.f64 x)
(exp.f64 (*.f64 x #s(literal 1 binary64)))
(pow.f64 (exp.f64 x) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))

eval55.0ms (0.7%)

Memory: -13.1MiB live, 105.5MiB allocated
Compiler: Compiled 15 107 to 1 438 computations (90.5% saved)

prune134.0ms (1.6%)

Memory

-14.2MiB live, 109.8MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	410	9	419
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	411	9	420

Accuracy

99.7%

Counts

420 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	42.9%	(/.f64 (fma.f64 x (.f64 y (.f64 x (.f64 x (.f64 y y)))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))))
▶	48.1%	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
▶	99.6%	(-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))
▶	93.5%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
	76.0%	(.f64 (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))) (.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))))))
▶	78.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
	85.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
▶	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
	48.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))

Compiler

Compiled 358 to 178 computations (50.3% saved)

simplify279.0ms (3.4%)

Memory

32.2MiB live, 392.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log1p.f64 (exp.f64 x))
✓	cost-diff	0	(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
✓	cost-diff	0	(-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y))))))
✓	cost-diff	0	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
✓	cost-diff	0	(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
✓	cost-diff	0	(-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)
✓	cost-diff	0	(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(*.f64 x y)
✓	cost-diff	0	#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
✓	cost-diff	0	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
✓	cost-diff	0	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
✓	cost-diff	0	(neg.f64 y)
✓	cost-diff	0	(*.f64 x (neg.f64 y))
✓	cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
✓	cost-diff	0	(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
✓	cost-diff	256	(-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))
✓	cost-diff	768	(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
✓	cost-diff	6400	(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))

Rules

7 006×	`lower-fma.f32`
6 998×	`lower-fma.f64`
6 680×	`lower-*.f32`
6 664×	`lower-*.f64`
2 008×	`lower--.f32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	45	307
0	78	307
1	143	307
2	319	283
3	1202	271
4	3515	267
5	6729	256
0	8022	256

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(expm1.f64 x)
x
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(*.f64 x y)
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
(*.f64 x (neg.f64 y))
x
(neg.f64 y)
y
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x y)
x
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
x
(-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)
(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
y
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
(-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y))))))
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
(log1p.f64 (exp.f64 x))
(exp.f64 x)
x
#s(literal 4 binary64)
(.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y)))))
(.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))
(.f64 x (.f64 y y))
(*.f64 y y)
y
(.f64 x (.f64 x (*.f64 y y)))
(.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (*.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))))
(fma.f64 x y (log1p.f64 (exp.f64 x)))
(fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
(-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(neg.f64 (neg.f64 (log1p.f64 (exp.f64 x))))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(neg.f64 (log1p.f64 (exp.f64 x)))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(expm1.f64 x)
x
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(*.f64 x y)
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
(*.f64 x (neg.f64 y))
x
(neg.f64 y)
y
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
#s(literal 2 binary64)
(*.f64 x y)
x
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64))))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64)))
x
(-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)
(fma.f64 x #s(literal 1/8 binary64) (-.f64 #s(literal 1/2 binary64) y))
(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
#s(literal 1/8 binary64)
#s(literal 1/2 binary64)
y
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 y (.f64 y (.f64 y y)))))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
(-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y))))))
(-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 y (.f64 y (*.f64 y y))))))))
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
(log1p.f64 (exp.f64 x))
(exp.f64 x)
x
#s(literal 4 binary64)
(.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y)))))
(.f64 x (.f64 x (.f64 x (.f64 x (.f64 y (.f64 y (*.f64 y y)))))))
(.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y))))
(.f64 x (.f64 x (.f64 x (.f64 y (.f64 y (.f64 y y))))))
(.f64 x (.f64 y y))
(*.f64 y y)
y
(.f64 x (.f64 x (*.f64 y y)))
(.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (*.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))))
(fma.f64 x y (log1p.f64 (exp.f64 x)))
(fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))
#s(literal 2 binary64)

localize184.0ms (2.2%)

Memory

-6.0MiB live, 190.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	95.4%	(.f64 x (.f64 x (*.f64 y y)))
✓	accuracy	95.2%	(.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y)))))
✓	accuracy	93.2%	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
✓	accuracy	89.7%	(.f64 x (.f64 y y))
✓	accuracy	100.0%	(-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
✓	accuracy	99.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
✓	accuracy	99.6%	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
✓	accuracy	99.0%	#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
✓	accuracy	100.0%	(*.f64 x (neg.f64 y))
✓	accuracy	100.0%	(neg.f64 y)
✓	accuracy	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
✓	accuracy	100.0%	(expm1.f64 x)
✓	accuracy	100.0%	(-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))
✓	accuracy	99.6%	(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
✓	accuracy	99.6%	(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))

Samples

46.0ms	166×	0	valid
37.0ms	90×	1	exit

Compiler

Compiled 343 to 41 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 16.0ms (26.6% of total)

adjust: 7.0ms (11.6% of total)

ival-log: 7.0ms (11.6% of total)

ival-add: 6.0ms (10% of total)

ival-expm1: 4.0ms (6.6% of total)

ival-sub: 4.0ms (6.6% of total)

ival-div: 3.0ms (5% of total)

ival-log1p: 3.0ms (5% of total)

ival-pow: 3.0ms (5% of total)

ival-exp: 2.0ms (3.3% of total)

ival-pow2: 2.0ms (3.3% of total)

ival-neg: 2.0ms (3.3% of total)

exact: 1.0ms (1.7% of total)

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

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

series110.0ms (1.3%)

Memory

-9.8MiB live, 104.9MiB allocated

Counts

24 → 432

Calls

Call 1

Inputs
#<alt (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))>
#<alt (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))>
#<alt (-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))>
#<alt (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))>
#<alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))>
#<alt (*.f64 x (neg.f64 y))>
#<alt (neg.f64 y)>
#<alt (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))>
#<alt (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))>
#<alt #s(approx (+ 1 (exp x)) #s(literal 2 binary64))>
#<alt (*.f64 x y)>
#<alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))>
#<alt (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))>
#<alt (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)>
#<alt (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))>
#<alt (/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))>
#<alt (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y))))))>
#<alt (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))>
#<alt (log1p.f64 (exp.f64 x))>
#<alt (expm1.f64 x)>
#<alt (log.f64 #s(literal 2 binary64))>
#<alt (.f64 x (.f64 y y))>
#<alt (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y)))))>
#<alt (.f64 x (.f64 x (*.f64 y y)))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (log 1/2)>
#<alt (+ (log 1/2) (* -1/2 x))>
#<alt (+ (log 1/2) (* x (- (* -1/8 x) 1/2)))>
#<alt (+ (log 1/2) (* x (- (* x (- (* 1/192 (pow x 2)) 1/8)) 1/2)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt (* -1 (log 1/2))>
#<alt (- (* x (- 1/2 y)) (log 1/2))>
#<alt (- (* x (- (+ 1/2 (* 1/8 x)) y)) (log 1/2))>
#<alt (- (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)) (log 1/2))>
#<alt (* -1 (* x y))>
#<alt (* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))>
#<alt (* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))>
#<alt (* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))>
#<alt (* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))>
#<alt (* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (* x y))>
#<alt (* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))>
#<alt (* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))>
#<alt (* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))>
#<alt (* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))>
#<alt (* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))>
#<alt (* -1 (log 1/2))>
#<alt (- (* 1/2 x) (log 1/2))>
#<alt (- (* x (+ 1/2 (* 1/8 x))) (log 1/2))>
#<alt (- (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) (log 1/2))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x y))>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (log 2)>
#<alt (+ (log 2) (* 1/2 x))>
#<alt (+ (log 2) (* x (+ 1/2 (* 1/8 x))))>
#<alt (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (+ 1 (exp x))>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (* x y)>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))>
#<alt (* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))>
#<alt (* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))>
#<alt (* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))>
#<alt (* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))>
#<alt (+ (log 2) (* x (+ 1/2 (* 1/8 x))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))>
#<alt (- 1/2 y)>
#<alt (- (+ 1/2 (* 1/8 x)) y)>
#<alt (- (+ 1/2 (* 1/8 x)) y)>
#<alt (- (+ 1/2 (* 1/8 x)) y)>
#<alt (* 1/8 x)>
#<alt (* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))>
#<alt (* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))>
#<alt (* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))>
#<alt (* 1/8 x)>
#<alt (* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))>
#<alt (* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))>
#<alt (* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))>
#<alt (+ 1/2 (* 1/8 x))>
#<alt (+ 1/2 (+ (* -1 y) (* 1/8 x)))>
#<alt (+ 1/2 (+ (* -1 y) (* 1/8 x)))>
#<alt (+ 1/2 (+ (* -1 y) (* 1/8 x)))>
#<alt (* -1 y)>
#<alt (* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))>
#<alt (* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))>
#<alt (* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))>
#<alt 1/2>
#<alt (+ 1/2 (* 1/8 x))>
#<alt (+ 1/2 (* 1/8 x))>
#<alt (+ 1/2 (* 1/8 x))>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* 1/8 x)>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1/8 (* 1/2 (/ 1 x))))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (pow (log 2) 4)>
#<alt (+ (* 2 (* x (pow (log 2) 3))) (pow (log 2) 4))>
#<alt (+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (pow (log 2) 2))))) (pow (log 2) 4))>
#<alt (+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (+ (* x (+ (* 1/4 (pow (log 2) 2)) (* 2 (* (log 2) (+ 1/4 (* 1/4 (log 2))))))) (pow (log 2) 2)))))) (pow (log 2) 4))>
#<alt (* -1 (* (pow x 4) (pow y 4)))>
#<alt (* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))>
#<alt (* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))>
#<alt (* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))>
#<alt (* -1 (* (pow x 4) (pow y 4)))>
#<alt (* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))>
#<alt (* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))>
#<alt (* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (+ (* -1 (* (pow x 4) (pow y 4))) (pow (log (+ 1 (exp x))) 4))>
#<alt (+ (* -1 (* (pow x 4) (pow y 4))) (pow (log (+ 1 (exp x))) 4))>
#<alt (+ (* -1 (* (pow x 4) (pow y 4))) (pow (log (+ 1 (exp x))) 4))>
#<alt (* -1 (* (pow x 4) (pow y 4)))>
#<alt (* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))>
#<alt (* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))>
#<alt (* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))>
#<alt (* -1 (* (pow x 4) (pow y 4)))>
#<alt (* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))>
#<alt (* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))>
#<alt (* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))>
#<alt (pow (log 2) 4)>
#<alt (+ (* 2 (* x (pow (log 2) 3))) (pow (log 2) 4))>
#<alt (+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (pow (log 2) 2))))) (pow (log 2) 4))>
#<alt (+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (+ (* x (+ (* 1/4 (pow (log 2) 2)) (* 2 (* (log 2) (+ 1/4 (* 1/4 (log 2))))))) (pow (log 2) 2)))))) (pow (log 2) 4))>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (pow (log (+ 1 (exp x))) 4)>
#<alt (log 2)>
#<alt (+ (log 2) (* 1/2 x))>
#<alt (+ (log 2) (* x (+ 1/2 (* 1/8 x))))>
#<alt (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* x (pow y 2))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 4) (pow y 4))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>
#<alt (* (pow x 2) (pow y 2))>

Calls

108 calls:

Time	Variable		Point	Expression
39.0ms	x	@	-inf	(log (/ (- (exp x) 1) (- (exp (+ x x)) 1)))
30.0ms	x	@	inf	(log (/ (- (exp x) 1) (- (exp (+ x x)) 1)))
5.0ms	y	@	0	(- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y))))))
4.0ms	y	@	0	(- (neg (log (/ (- (exp x) 1) (- (exp (+ x x)) 1)))) (* x y))
4.0ms	x	@	0	(* x (* (* x (* y y)) (* x (* x (* y y)))))

simplify335.0ms (4%)

Memory

-1.7MiB live, 376.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 786×	`lower-fma.f64`
7 786×	`lower-fma.f32`
3 654×	`lower-+.f64`
3 654×	`lower-+.f32`
3 550×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	416	4067
1	1314	3963
2	4317	3889
0	8436	3346

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 431

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(log 1/2)
(+ (log 1/2) (* -1/2 x))
(+ (log 1/2) (* x (- (* -1/8 x) 1/2)))
(+ (log 1/2) (* x (- (* x (- (* 1/192 (pow x 2)) 1/8)) 1/2)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(* -1 (log 1/2))
(- (* x (- 1/2 y)) (log 1/2))
(- (* x (- (+ 1/2 (* 1/8 x)) y)) (log 1/2))
(- (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)) (log 1/2))
(* -1 (* x y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(* -1 (* x y))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (* x y))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(* -1 (* x y))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(* -1 (log 1/2))
(- (* 1/2 x) (log 1/2))
(- (* x (+ 1/2 (* 1/8 x))) (log 1/2))
(- (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) (log 1/2))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(log 2)
(+ (log 2) (* 1/2 x))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(+ 1 (exp x))
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(* x y)
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(* 1/8 (pow x 2))
(* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))
(* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))
(* 1/8 (pow x 2))
(* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(* -1 (* x y))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(- 1/2 y)
(- (+ 1/2 (* 1/8 x)) y)
(- (+ 1/2 (* 1/8 x)) y)
(- (+ 1/2 (* 1/8 x)) y)
(* 1/8 x)
(* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* 1/8 x)
(* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))
(* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))
(* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))
(+ 1/2 (* 1/8 x))
(+ 1/2 (+ (* -1 y) (* 1/8 x)))
(+ 1/2 (+ (* -1 y) (* 1/8 x)))
(+ 1/2 (+ (* -1 y) (* 1/8 x)))
(* -1 y)
(* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))
(* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))
(* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))
1/2
(+ 1/2 (* 1/8 x))
(+ 1/2 (* 1/8 x))
(+ 1/2 (* 1/8 x))
(* 1/8 x)
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* 1/8 x)
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(* x (+ 1/8 (* 1/2 (/ 1 x))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))
(pow (log 2) 4)
(+ (* 2 (* x (pow (log 2) 3))) (pow (log 2) 4))
(+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (pow (log 2) 2))))) (pow (log 2) 4))
(+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (+ (* x (+ (* 1/4 (pow (log 2) 2)) (* 2 (* (log 2) (+ 1/4 (* 1/4 (log 2))))))) (pow (log 2) 2)))))) (pow (log 2) 4))
(* -1 (* (pow x 4) (pow y 4)))
(* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))
(* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))
(* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))
(* -1 (* (pow x 4) (pow y 4)))
(* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))
(* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))
(* (pow x 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow x 4)) (pow y 4)))
(pow (log (+ 1 (exp x))) 4)
(+ (* -1 (* (pow x 4) (pow y 4))) (pow (log (+ 1 (exp x))) 4))
(+ (* -1 (* (pow x 4) (pow y 4))) (pow (log (+ 1 (exp x))) 4))
(+ (* -1 (* (pow x 4) (pow y 4))) (pow (log (+ 1 (exp x))) 4))
(* -1 (* (pow x 4) (pow y 4)))
(* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))
(* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))
(* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))
(* -1 (* (pow x 4) (pow y 4)))
(* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))
(* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))
(* (pow y 4) (- (/ (pow (log (+ 1 (exp x))) 4) (pow y 4)) (pow x 4)))
(pow (log 2) 4)
(+ (* 2 (* x (pow (log 2) 3))) (pow (log 2) 4))
(+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (pow (log 2) 2))))) (pow (log 2) 4))
(+ (* x (+ (* 2 (pow (log 2) 3)) (* x (+ (* 2 (* (pow (log 2) 2) (+ 1/4 (* 1/4 (log 2))))) (+ (* x (+ (* 1/4 (pow (log 2) 2)) (* 2 (* (log 2) (+ 1/4 (* 1/4 (log 2))))))) (pow (log 2) 2)))))) (pow (log 2) 4))
(pow (log (+ 1 (exp x))) 4)
(pow (log (+ 1 (exp x))) 4)
(pow (log (+ 1 (exp x))) 4)
(pow (log (+ 1 (exp x))) 4)
(pow (log (+ 1 (exp x))) 4)
(pow (log (+ 1 (exp x))) 4)
(pow (log (+ 1 (exp x))) 4)
(pow (log (+ 1 (exp x))) 4)
(log 2)
(+ (log 2) (* 1/2 x))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* x (pow y 2))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 4) (pow y 4))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))
(* (pow x 2) (pow y 2))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(fma.f64 #s(literal -1/4 binary64) x #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/480 binary64) #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(log 1/2)
(log.f64 #s(literal 1/2 binary64))
(+ (log 1/2) (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (* x (- (* x (- (* 1/192 (pow x 2)) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 (*.f64 x x) #s(literal 1/192 binary64) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) (log.f64 #s(literal 1/2 binary64)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(* -1 (log 1/2))
(neg.f64 (log.f64 #s(literal 1/2 binary64)))
(- (* x (- 1/2 y)) (log 1/2))
(-.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 1/2 binary64)))
(- (* x (- (+ 1/2 (* 1/8 x)) y)) (log 1/2))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (neg.f64 (log.f64 #s(literal 1/2 binary64))))
(- (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)) (log 1/2))
(-.f64 (.f64 x (-.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) y)) (log.f64 #s(literal 1/2 binary64)))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (fma.f64 x y (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (fma.f64 x y (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (fma.f64 x y (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 y)) x))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 y)) x))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 y)) x))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 y)) x))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 y)) x))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 y)) x))
(* -1 (log 1/2))
(neg.f64 (log.f64 #s(literal 1/2 binary64)))
(- (* 1/2 x) (log 1/2))
(-.f64 (*.f64 #s(literal 1/2 binary64) x) (log.f64 #s(literal 1/2 binary64)))
(- (* x (+ 1/2 (* 1/8 x))) (log 1/2))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (neg.f64 (log.f64 #s(literal 1/2 binary64))))
(- (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) (log 1/2))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (neg.f64 (log.f64 #s(literal 1/2 binary64))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* x (- 1/2 y)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(fma.f64 x (-.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(* -1 (* x y))
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(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
(pow (log (+ 1 (exp x))) 4)
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
(pow (log (+ 1 (exp x))) 4)
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
(pow (log (+ 1 (exp x))) 4)
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* 1/2 x))
(fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x x) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* x (pow y 2))
(.f64 x (.f64 y y))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 4) (pow y 4))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (pow.f64 y #s(literal 4 binary64)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))
(* (pow x 2) (pow y 2))
(.f64 x (.f64 x (*.f64 y y)))

rewrite455.0ms (5.5%)

Memory

-14.1MiB live, 584.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 478×	`lower-/.f32`
4 474×	`lower-/.f64`
4 338×	`lower-*.f32`
4 322×	`lower-*.f64`
3 472×	`lower-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	45	221
0	78	199
1	308	152
2	2493	148
0	8814	148

Stop Event

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

Counts

24 → 938

Calls

Call 1

Inputs
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
(*.f64 x (neg.f64 y))
(neg.f64 y)
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
(*.f64 x y)
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)
(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
(-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y))))))
(pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64))
(log1p.f64 (exp.f64 x))
(expm1.f64 x)
(log.f64 #s(literal 2 binary64))
(.f64 x (.f64 y y))
(.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (*.f64 y y)))))
(.f64 x (.f64 x (*.f64 y y)))

Outputs
(+.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(exp.f64 (*.f64 (log1p.f64 (exp.f64 x)) #s(literal -1 binary64)))
(-.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))
(-.f64 (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (expm1.f64 (+.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (expm1.f64 (+.f64 x x))))
(-.f64 (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x)))) (expm1.f64 (+.f64 x x))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x)))) (expm1.f64 (+.f64 x x))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 (/.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (expm1.f64 (+.f64 x x)))) (/.f64 (expm1.f64 x) (neg.f64 (expm1.f64 (+.f64 x x)))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (expm1.f64 (+.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))))))
(-.f64 (/.f64 (.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal 2 binary64))) (/.f64 (.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (exp.f64 (+.f64 x x)) (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal -3 binary64))) (+.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal -2 binary64)) (.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))))) (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal -3 binary64)) (+.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal -2 binary64)) (*.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))))))
(-.f64 (/.f64 (pow.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) #s(literal 2 binary64)) (+.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))) (/.f64 (pow.f64 (expm1.f64 (+.f64 x x)) #s(literal -2 binary64)) (+.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 x) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (/.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (/.f64 (exp.f64 x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 (exp.f64 x) (expm1.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(fma.f64 (/.f64 (exp.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x)))))
(neg.f64 (/.f64 (expm1.f64 x) (neg.f64 (expm1.f64 (+.f64 x x)))))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 x)) (expm1.f64 (+.f64 x x))))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (+.f64 x x)) (*.f64 (expm1.f64 (+.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x)))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 x)) (neg.f64 (expm1.f64 (+.f64 x x))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (*.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 x)))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (*.f64 (expm1.f64 (+.f64 x x)) (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) #s(literal 1 binary64))))
(/.f64 (.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (expm1.f64 (+.f64 x x))))
(/.f64 (.f64 (expm1.f64 (+.f64 x x)) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)) (exp.f64 (+.f64 x x))) (expm1.f64 (+.f64 x x))))
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(/.f64 (neg.f64 (neg.f64 (expm1.f64 x))) (neg.f64 (neg.f64 (expm1.f64 (+.f64 x x)))))
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(pow.f64 (*.f64 x y) #s(literal 4 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 y y))) #s(literal 2 binary64))
(.f64 x (.f64 (.f64 x y) (.f64 y (.f64 x (.f64 x (*.f64 y y))))))
(.f64 (.f64 y y) (pow.f64 (.f64 x (.f64 x y)) #s(literal 2 binary64)))
(.f64 (.f64 x (.f64 y y)) (.f64 (.f64 x (.f64 x (*.f64 y y))) x))
(.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 x (*.f64 y y)))))
(.f64 (.f64 (.f64 x y) (.f64 y (.f64 x (.f64 x (*.f64 y y))))) x)
(.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x (.f64 x (*.f64 y y))))
(.f64 (.f64 x x) (.f64 y (.f64 y (.f64 x (.f64 x (*.f64 y y))))))
(.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 y y) (*.f64 y y)))
(.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 x x) (*.f64 x x)))
(.f64 (.f64 y (.f64 y (.f64 x (.f64 x (.f64 y y))))) (*.f64 x x))
(.f64 (.f64 (.f64 x (.f64 x (.f64 y y))) x) (.f64 x (*.f64 y y)))
(.f64 (.f64 x (.f64 x (.f64 x (.f64 y y)))) (.f64 x (*.f64 y y)))
(.f64 (.f64 (.f64 x (.f64 x (.f64 y y))) (.f64 x x)) (*.f64 y y))
(.f64 (pow.f64 (.f64 x (.f64 x y)) #s(literal 2 binary64)) (.f64 y y))
(.f64 (pow.f64 (.f64 (.f64 x x) y) #s(literal 2 binary64)) (.f64 y y))
(exp.f64 (.f64 (log.f64 (.f64 x y)) #s(literal 2 binary64)))
(pow.f64 (*.f64 x y) #s(literal 2 binary64))
(pow.f64 (neg.f64 (*.f64 x y)) #s(literal 2 binary64))
(.f64 x (.f64 x (*.f64 y y)))
(.f64 y (.f64 x (*.f64 x y)))
(.f64 (.f64 x y) (*.f64 x y))
(.f64 (.f64 y y) (*.f64 x x))
(.f64 (.f64 x (*.f64 y y)) x)
(.f64 (.f64 x x) (*.f64 y y))
(.f64 (neg.f64 (.f64 x y)) (neg.f64 (*.f64 x y)))
(.f64 (.f64 (*.f64 x y) x) y)
(.f64 (.f64 x (*.f64 x y)) y)
(.f64 (.f64 (*.f64 x x) y) y)

eval204.0ms (2.5%)

Memory: 21.1MiB live, 438.1MiB allocated
Compiler: Compiled 59 546 to 3 710 computations (93.8% saved)

prune187.0ms (2.2%)

Memory

-4.3MiB live, 324.7MiB allocated

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	1 573	8	1 581
Fresh	4	0	4
Picked	2	3	5
Done	0	0	0
Total	1 579	11	1 590

Accuracy

99.7%

Counts

1 590 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.0%	(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
✓	93.5%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
▶	85.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
▶	99.6%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
	48.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
✓	78.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
▶	13.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
✓	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
	21.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
▶	8.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
	77.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (*.f64 y (+.f64 (neg.f64 x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))) y)))))

Compiler

Compiled 257 to 157 computations (38.9% saved)

simplify302.0ms (3.6%)

Memory

31.5MiB live, 386.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))
✓	cost-diff	0	(log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))
✓	cost-diff	0	(neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
✓	cost-diff	128	(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
✓	cost-diff	0	(log.f64 #s(literal 2 binary64))
✓	cost-diff	0	(-.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
✓	cost-diff	64	(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
✓	cost-diff	192	(+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))
✓	cost-diff	320	(*.f64 #s(literal 0 binary64) y)
✓	cost-diff	1664	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	cost-diff	0	#s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
✓	cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
✓	cost-diff	0	(/.f64 (log1p.f64 (exp.f64 x)) x)
✓	cost-diff	0	(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
✓	cost-diff	0	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
✓	cost-diff	384	(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))

Rules

8 890×	`lower-fma.f32`
8 882×	`lower-fma.f64`
6 384×	`lower-*.f32`
6 370×	`lower-*.f64`
1 804×	`distribute-lft-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	426
0	99	390
1	198	387
2	467	357
3	1627	349
4	5074	349
0	8159	330

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
x
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(/.f64 (log1p.f64 (exp.f64 x)) x)
(log1p.f64 (exp.f64 x))
(exp.f64 x)
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
(.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y)))))
x
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
#s(literal 0 binary64)
(.f64 y (.f64 y y))
y
(*.f64 y y)
(+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))
(fma.f64 y y (*.f64 #s(literal 0 binary64) y))
(*.f64 #s(literal 0 binary64) y)
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
x
(-.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
(neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
(log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))
(/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))
#s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(*.f64 x x)
x
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(*.f64 x y)
y

Outputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 (log1p.f64 (exp.f64 x)) #s(literal 1 binary64) (*.f64 x (neg.f64 y))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(fma.f64 (log1p.f64 (exp.f64 x)) #s(literal 1 binary64) (*.f64 x (neg.f64 y)))
x
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(/.f64 (log1p.f64 (exp.f64 x)) x)
(log1p.f64 (exp.f64 x))
(exp.f64 x)
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 x (.f64 x #s(literal 1/8 binary64)))))
#s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
#s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 x (.f64 x #s(literal 1/8 binary64))))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(*.f64 x x)
x
#s(literal 1/8 binary64)
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
(.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y)))))
(*.f64 x (neg.f64 y))
x
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))
(neg.f64 y)
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
(.f64 y (.f64 y (neg.f64 y)))
#s(literal 0 binary64)
(.f64 y (.f64 y y))
y
(*.f64 y y)
(+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))
(*.f64 y y)
(fma.f64 y y (*.f64 #s(literal 0 binary64) y))
(*.f64 y y)
(*.f64 #s(literal 0 binary64) y)
#s(literal 0 binary64)
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
x
(-.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
(neg.f64 (fma.f64 x y (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))))
(neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
(log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))
(/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))
#s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(*.f64 x x)
x
(fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64))
#s(literal 1/6 binary64)
#s(literal 1/2 binary64)
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(*.f64 x y)
y

localize191.0ms (2.3%)

Memory

-15.3MiB live, 234.2MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
✓	accuracy	99.6%	(log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))
✓	accuracy	99.6%	(/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))
✓	accuracy	99.6%	#s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))
✓	accuracy	100.0%	(-.f64 #s(literal 1/2 binary64) y)
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
✓	accuracy	99.6%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
✓	accuracy	100.0%	(*.f64 #s(literal 0 binary64) y)
✓	accuracy	99.9%	(.f64 y (.f64 y y))
✓	accuracy	60.5%	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))
✓	accuracy	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
✓	accuracy	100.0%	(.f64 (.f64 x x) #s(literal 1/8 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
✓	accuracy	37.7%	#s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
✓	accuracy	100.0%	(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
✓	accuracy	99.9%	(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
✓	accuracy	99.8%	(/.f64 (log1p.f64 (exp.f64 x)) x)
✓	accuracy	99.6%	(log1p.f64 (exp.f64 x))

Samples

67.0ms	166×	0	valid
49.0ms	90×	1	exit

Compiler

Compiled 358 to 58 computations (83.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 94.0ms

ival-mult: 26.0ms (27.7% of total)

ival-log: 12.0ms (12.8% of total)

adjust: 11.0ms (11.7% of total)

ival-add: 10.0ms (10.6% of total)

ival-sub: 8.0ms (8.5% of total)

ival-div: 6.0ms (6.4% of total)

const: 4.0ms (4.3% of total)

ival-expm1: 3.0ms (3.2% of total)

ival-log1p: 3.0ms (3.2% of total)

ival-pow: 3.0ms (3.2% of total)

ival-pow2: 3.0ms (3.2% of total)

ival-exp: 2.0ms (2.1% of total)

exact: 1.0ms (1.1% of total)

ival-neg: 1.0ms (1.1% of total)

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

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

series30.0ms (0.4%)

Memory

8.7MiB live, 46.5MiB allocated

Counts

24 → 384

Calls

Call 1

Inputs
#<alt (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))>
#<alt #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))>
#<alt (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)>
#<alt (/.f64 (log1p.f64 (exp.f64 x)) x)>
#<alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))>
#<alt #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))>
#<alt (.f64 (.f64 x x) #s(literal 1/8 binary64))>
#<alt (*.f64 x x)>
#<alt (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))>
#<alt (*.f64 #s(literal 0 binary64) y)>
#<alt (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))>
#<alt (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))>
#<alt #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))>
#<alt (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))>
#<alt (-.f64 #s(literal 1/2 binary64) y)>
#<alt (log.f64 #s(literal 2 binary64))>
#<alt (-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))>
#<alt (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))>
#<alt (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))>
#<alt (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))>
#<alt (log1p.f64 (exp.f64 x))>
#<alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))>
#<alt (.f64 y (.f64 y y))>
#<alt #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))>

Outputs
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (/ (log 2) x)>
#<alt (/ (+ (log 2) (* x (- 1/2 y))) x)>
#<alt (/ (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y))) x)>
#<alt (/ (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y))) x)>
#<alt (* -1 y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (* -1 y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (+ (* -1 y) (/ (log (+ 1 (exp x))) x))>
#<alt (+ (* -1 y) (/ (log (+ 1 (exp x))) x))>
#<alt (+ (* -1 y) (/ (log (+ 1 (exp x))) x))>
#<alt (* -1 y)>
#<alt (* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))>
#<alt (* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))>
#<alt (* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))>
#<alt (/ (log 2) x)>
#<alt (/ (+ (log 2) (* 1/2 x)) x)>
#<alt (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) x)>
#<alt (/ (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))>
#<alt (* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))>
#<alt (* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))>
#<alt (* 1/8 (pow x 2))>
#<alt (* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))>
#<alt (* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))>
#<alt (* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))>
#<alt (+ (log 2) (* x (+ 1/2 (* 1/8 x))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (* 1/8 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt (* -1 y)>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (* -1 (pow y 3))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (* x (- 1/2 y))>
#<alt (* x (- (+ 1/2 (/ (log 2) x)) y))>
#<alt (* x (- (+ 1/2 (/ (log 2) x)) y))>
#<alt (* x (- (+ 1/2 (/ (log 2) x)) y))>
#<alt (* x (- 1/2 y))>
#<alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))>
#<alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))>
#<alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))>
#<alt (+ (log 2) (* 1/2 x))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))>
#<alt (* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))>
#<alt (* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1 y))>
#<alt (+ 1/2 (* -1 y))>
#<alt (+ 1/2 (* -1 y))>
#<alt (* -1 y)>
#<alt (* y (- (* 1/2 (/ 1 y)) 1))>
#<alt (* y (- (* 1/2 (/ 1 y)) 1))>
#<alt (* y (- (* 1/2 (/ 1 y)) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (- 1 (* 1/2 (/ 1 y)))))>
#<alt (* -1 (* y (- 1 (* 1/2 (/ 1 y)))))>
#<alt (* -1 (* y (- 1 (* 1/2 (/ 1 y)))))>
#<alt (* -1 (log 1/2))>
#<alt (- (* x (- 1/2 y)) (log 1/2))>
#<alt (- (* x (- (+ 1/2 (* 1/8 x)) y)) (log 1/2))>
#<alt (- (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)) (log 1/2))>
#<alt (* -1 (* x y))>
#<alt (* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))>
#<alt (* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))>
#<alt (* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))>
#<alt (* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))>
#<alt (* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (* x y))>
#<alt (* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))>
#<alt (* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))>
#<alt (* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))>
#<alt (* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))>
#<alt (* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))>
#<alt (* -1 (log 1/2))>
#<alt (- (* 1/2 x) (log 1/2))>
#<alt (- (* x (+ 1/2 (* 1/8 x))) (log 1/2))>
#<alt (- (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) (log 1/2))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))>
#<alt (log 1/2)>
#<alt (+ (log 1/2) (* -1/2 x))>
#<alt (+ (log 1/2) (* x (- (* -1/8 x) 1/2)))>
#<alt (+ (log 1/2) (* x (- (* x (- (* 1/192 (pow x 2)) 1/8)) 1/2)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/4 x))>
#<alt (+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))>
#<alt (+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (* 2 x)) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))>
#<alt (log 2)>
#<alt (+ (log 2) (* 1/2 x))>
#<alt (+ (log 2) (* x (+ 1/2 (* 1/8 x))))>
#<alt (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* x (- (/ (log (+ 1 (exp x))) x) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* y (- (/ (log (+ 1 (exp x))) y) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt (pow y 3)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 x)))>
#<alt (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))>
#<alt (* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>
#<alt (- (exp x) 1)>

Calls

96 calls:

Time	Variable		Point	Expression
11.0ms	x	@	inf	(/ (log (+ 1 (exp x))) x)
5.0ms	x	@	-inf	(/ (log (+ 1 (exp x))) x)
1.0ms	x	@	0	(+ (* x (- 1/2 y)) (log 2))
1.0ms	x	@	-inf	(* x (- (/ (log (+ 1 (exp x))) x) y))
0.0ms	x	@	inf	(* x (- (/ (log (+ 1 (exp x))) x) y))

simplify406.0ms (4.9%)

Memory

-7.3MiB live, 552.1MiB allocated

Algorithm

1×	egg-herbie

Rules

7 614×	`lower-fma.f64`
7 614×	`lower-fma.f32`
3 478×	`lower-+.f64`
3 478×	`lower-+.f32`
3 252×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	395	3915
1	1245	3742
2	4112	3632
0	8371	3079

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 383

Calls

Call 1

Inputs
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))
(/ (log 2) x)
(/ (+ (log 2) (* x (- 1/2 y))) x)
(/ (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y))) x)
(/ (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y))) x)
(* -1 y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(* -1 y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(/ (log (+ 1 (exp x))) x)
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(* -1 y)
(* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))
(* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))
(* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))
(* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))
(* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))
(/ (log 2) x)
(/ (+ (log 2) (* 1/2 x)) x)
(/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) x)
(/ (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(* 1/8 (pow x 2))
(* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))
(* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))
(* 1/8 (pow x 2))
(* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(* -1 (* x y))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(* 1/8 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
0
0
0
0
0
0
0
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0
0
0
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
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(pow y 2)
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(pow y 2)
(pow y 2)
(pow y 2)
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- 1/2 y)))
(* x (- 1/2 y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- 1/2 y))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(+ (log 2) (* 1/2 x))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(* -1 (* x y))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
1/2
(+ 1/2 (* -1 y))
(+ 1/2 (* -1 y))
(+ 1/2 (* -1 y))
(* -1 y)
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* -1 y)
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (log 1/2))
(- (* x (- 1/2 y)) (log 1/2))
(- (* x (- (+ 1/2 (* 1/8 x)) y)) (log 1/2))
(- (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)) (log 1/2))
(* -1 (* x y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(* x (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) x)) y))
(* -1 (* x y))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (* x y))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(* -1 (* x y))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(* -1 (log 1/2))
(- (* 1/2 x) (log 1/2))
(- (* x (+ 1/2 (* 1/8 x))) (log 1/2))
(- (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) (log 1/2))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(log 1/2)
(+ (log 1/2) (* -1/2 x))
(+ (log 1/2) (* x (- (* -1/8 x) 1/2)))
(+ (log 1/2) (* x (- (* x (- (* 1/192 (pow x 2)) 1/8)) 1/2)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
1/2
(+ 1/2 (* -1/4 x))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(log 2)
(+ (log 2) (* 1/2 x))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
x
(* x (+ 1 (* 1/2 x)))
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)
(- (exp x) 1)

Outputs
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* x (- 1/2 y)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(fma.f64 x (-.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* x (- 1/2 y)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
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(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* -1 (* x (- (/ (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))) x) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) (neg.f64 x)) y))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (fma.f64 x y (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (fma.f64 x y (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))))
(- (* -1 (* x y)) (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (fma.f64 x y (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(*.f64 y (-.f64 (neg.f64 x) (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) y)))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(*.f64 y (-.f64 (neg.f64 x) (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) y)))
(* y (- (* -1 (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y)) x))
(*.f64 y (-.f64 (neg.f64 x) (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) y)))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(*.f64 y (-.f64 (neg.f64 x) (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) y)))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(*.f64 y (-.f64 (neg.f64 x) (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) y)))
(* -1 (* y (- (/ (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))) y) (* -1 x))))
(*.f64 y (-.f64 (neg.f64 x) (/.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))) y)))
(* -1 (log 1/2))
(neg.f64 (log.f64 #s(literal 1/2 binary64)))
(- (* 1/2 x) (log 1/2))
(-.f64 (*.f64 x #s(literal 1/2 binary64)) (log.f64 #s(literal 1/2 binary64)))
(- (* x (+ 1/2 (* 1/8 x))) (log 1/2))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (neg.f64 (log.f64 #s(literal 1/2 binary64))))
(- (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) (log 1/2))
(-.f64 (.f64 x (fma.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64))) (log.f64 #s(literal 1/2 binary64)))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (* 2 x)) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(* -1 (log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))))
(neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))))
(log 1/2)
(log.f64 #s(literal 1/2 binary64))
(+ (log 1/2) (* -1/2 x))
(fma.f64 x #s(literal -1/2 binary64) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (* x (- (* -1/8 x) 1/2)))
(fma.f64 x (fma.f64 x #s(literal -1/8 binary64) #s(literal -1/2 binary64)) (log.f64 #s(literal 1/2 binary64)))
(+ (log 1/2) (* x (- (* x (- (* 1/192 (pow x 2)) 1/8)) 1/2)))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/192 binary64)) #s(literal -1/8 binary64)) #s(literal -1/2 binary64)) (log.f64 #s(literal 1/2 binary64)))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (* 2 x)) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
(log (/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1)))
(log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/4 x))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* 1/48 (pow x 2)) 1/4)))
(fma.f64 x (fma.f64 x (*.f64 x #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(+ 1/2 (* x (- (* (pow x 2) (+ 1/48 (* -1/480 (pow x 2)))) 1/4)))
(fma.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/480 binary64) #s(literal 1/48 binary64)) #s(literal -1/4 binary64)) #s(literal 1/2 binary64))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (* 2 x)) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(/ (- (exp x) 1) (- (exp (neg (* -2 x))) 1))
(/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x)))
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* x (- 1/2 y)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(fma.f64 x (-.f64 (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* x y))
(*.f64 y (neg.f64 x))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
x
(* x (+ 1 (* 1/2 x)))
(fma.f64 x (*.f64 x #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))
(fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)
(* x (+ 1 (* x (+ 1/2 (* x (+ 1/6 (* 1/24 x)))))))
(fma.f64 (*.f64 x x) (fma.f64 x (fma.f64 x #s(literal 1/24 binary64) #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)
(- (exp x) 1)
(expm1.f64 x)

rewrite60.0ms (0.7%)

Memory

-14.5MiB live, 105.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

200×	`lower-*.f32`
186×	`lower-*.f64`
174×	`lower-+.f32`
170×	`lower-+.f64`
136×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	356
0	99	331
0	455	313

Stop Event

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

Counts

24 → 78

Calls

Call 1

Inputs
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(/.f64 (log1p.f64 (exp.f64 x)) x)
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64)))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(*.f64 x x)
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y))))
(*.f64 #s(literal 0 binary64) y)
(+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(-.f64 #s(literal 1/2 binary64) y)
(log.f64 #s(literal 2 binary64))
(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
(neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
(log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))
(/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))
(log1p.f64 (exp.f64 x))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
(.f64 y (.f64 y y))
#s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))

Outputs
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(*.f64 (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y) x)
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
(+.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) (neg.f64 y))
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(fma.f64 (log1p.f64 (exp.f64 x)) (/.f64 #s(literal 1 binary64) x) (neg.f64 y))
(/.f64 (-.f64 (pow.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) #s(literal 3 binary64)) (.f64 y (.f64 y y))) (fma.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) (/.f64 (log1p.f64 (exp.f64 x)) x) (fma.f64 y y (*.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))))
(/.f64 (-.f64 (.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) (/.f64 (log1p.f64 (exp.f64 x)) x)) (.f64 y y)) (+.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(/.f64 #s(literal 1 binary64) (/.f64 x (log1p.f64 (exp.f64 x))))
(/.f64 (log1p.f64 (exp.f64 x)) x)
(/.f64 (neg.f64 (log1p.f64 (exp.f64 x))) (neg.f64 x))
(*.f64 (log1p.f64 (exp.f64 x)) (/.f64 #s(literal 1 binary64) x))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 x (.f64 x #s(literal 1/8 binary64)))))
#s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 x (.f64 x #s(literal 1/8 binary64))))
(.f64 x (.f64 x #s(literal 1/8 binary64)))
(.f64 #s(literal 1/8 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/8 binary64))
(pow.f64 x #s(literal 2 binary64))
(*.f64 x x)
(-.f64 (/.f64 #s(literal 0 binary64) (fma.f64 y y #s(literal 0 binary64))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 y y #s(literal 0 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 0 binary64)) (neg.f64 (.f64 y (.f64 y y)))))
(/.f64 (neg.f64 (.f64 y (.f64 y y))) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 (neg.f64 (neg.f64 (.f64 y (.f64 y y)))) (neg.f64 (fma.f64 y y #s(literal 0 binary64))))
(.f64 (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
#s(literal 0 binary64)
(+.f64 #s(literal 0 binary64) (*.f64 y y))
(+.f64 #s(literal 0 binary64) (fma.f64 y y #s(literal 0 binary64)))
(+.f64 (*.f64 y y) #s(literal 0 binary64))
(+.f64 (fma.f64 y y #s(literal 0 binary64)) #s(literal 0 binary64))
(fma.f64 y y #s(literal 0 binary64))
(fma.f64 y (+.f64 y #s(literal 0 binary64)) #s(literal 0 binary64))
(/.f64 (+.f64 (pow.f64 (.f64 y y) #s(literal 3 binary64)) #s(literal 0 binary64)) (fma.f64 (.f64 y y) (.f64 y y) (-.f64 #s(literal 0 binary64) (.f64 (*.f64 y y) #s(literal 0 binary64)))))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 (fma.f64 y y #s(literal 0 binary64)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64))) (.f64 #s(literal 0 binary64) (fma.f64 y y #s(literal 0 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 y y) (.f64 y y)) #s(literal 0 binary64)) (-.f64 (.f64 y y) #s(literal 0 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 y y #s(literal 0 binary64)) (fma.f64 y y #s(literal 0 binary64)))) (-.f64 #s(literal 0 binary64) (fma.f64 y y #s(literal 0 binary64))))
(*.f64 y (+.f64 y #s(literal 0 binary64)))
(+.f64 #s(literal 0 binary64) (neg.f64 (.f64 y (.f64 y y))))
(+.f64 #s(literal 0 binary64) (.f64 (neg.f64 y) (.f64 y y)))
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
(neg.f64 (.f64 y (.f64 y y)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 y (.f64 y y)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)) (.f64 #s(literal 0 binary64) (.f64 y (*.f64 y y))))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 y (.f64 y y)) (.f64 y (.f64 y y)))) (+.f64 #s(literal 0 binary64) (.f64 y (*.f64 y y))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
(+.f64 (log.f64 #s(literal 2 binary64)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
(+.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64)))
(/.f64 (+.f64 (pow.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) #s(literal 3 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (-.f64 (.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64))) (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64))))))
(/.f64 (-.f64 (.f64 (.f64 x (-.f64 #s(literal 1/2 binary64) y)) (.f64 x (-.f64 #s(literal 1/2 binary64) y))) (.f64 (log.f64 #s(literal 2 binary64)) (log.f64 #s(literal 2 binary64)))) (-.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64))))
(+.f64 #s(literal 1/2 binary64) (neg.f64 y))
(-.f64 #s(literal 1/2 binary64) y)
(/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 1/4 binary64) (fma.f64 y y (*.f64 #s(literal 1/2 binary64) y))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 y y)) (+.f64 #s(literal 1/2 binary64) y))
(log.f64 #s(literal 2 binary64))
(+.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (neg.f64 (.f64 x y)))
(+.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 (neg.f64 x) y))
(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
(fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))) (neg.f64 (.f64 x y)))
(fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))) (.f64 (neg.f64 x) y))
(/.f64 (-.f64 (pow.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) #s(literal 3 binary64)) (pow.f64 (.f64 x y) #s(literal 3 binary64))) (fma.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (fma.f64 (.f64 x y) (.f64 x y) (.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (*.f64 x y)))))
(/.f64 (-.f64 (.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))) (.f64 (.f64 x y) (.f64 x y))) (+.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y)))
(log.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
(neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
(.f64 #s(literal -1 binary64) (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))))
(log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))
(-.f64 (log.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))) (log.f64 (expm1.f64 (+.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (expm1.f64 (+.f64 x x)) #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))))
(/.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x)))
(/.f64 (neg.f64 #s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))) (neg.f64 (expm1.f64 (+.f64 x x))))
(.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (/.f64 #s(literal 1 binary64) (expm1.f64 (+.f64 x x))))
(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(log1p.f64 (exp.f64 x))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
(pow.f64 y #s(literal 3 binary64))
(.f64 y (.f64 y y))
(.f64 (.f64 y y) y)
#s(approx (- (exp x) 1) (fma.f64 (*.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x))

eval85.0ms (1%)

Memory: 15.2MiB live, 133.3MiB allocated
Compiler: Compiled 6 686 to 469 computations (93% saved)

prune73.0ms (0.9%)

Memory

-2.1MiB live, 73.2MiB allocated

Pruning

15 alts after pruning (9 fresh and 6 done)

	Pruned	Kept	Total
New	468	7	475
Fresh	1	2	3
Picked	2	3	5
Done	0	3	3
Total	471	15	486

Accuracy

99.7%

Counts

486 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.0%	(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
✓	93.5%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
✓	85.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
▶	48.2%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
▶	93.4%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
	48.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
▶	39.1%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
	85.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (log.f64 #s(literal 2 binary64)) x) y)))))
✓	78.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
	10.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
▶	13.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
▶	13.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
✓	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
	21.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
✓	8.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))

Compiler

Compiled 301 to 181 computations (39.9% saved)

simplify287.0ms (3.5%)

Memory

-20.1MiB live, 389.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 #s(literal 2 binary64))
✓	cost-diff	0	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
✓	cost-diff	0	(fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
✓	cost-diff	0	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
✓	cost-diff	0	(.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))))
✓	cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
✓	cost-diff	64	(fma.f64 y y #s(literal 0 binary64))
✓	cost-diff	1984	(.f64 (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))
✓	cost-diff	0	(.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
✓	cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
✓	cost-diff	64	(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
✓	cost-diff	0	(-.f64 #s(literal 1/2 binary64) y)
✓	cost-diff	0	(*.f64 x (-.f64 #s(literal 1/2 binary64) y))
✓	cost-diff	0	#s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
✓	cost-diff	0	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
✓	cost-diff	0	(/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x)
✓	cost-diff	0	(-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)
✓	cost-diff	0	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
✓	cost-diff	384	(*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))

Rules

6 516×	`lower-*.f32`
6 502×	`lower-*.f64`
6 036×	`lower-fma.f32`
6 032×	`lower-fma.f64`
1 742×	`distribute-rgt-neg-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	469
0	76	416
1	159	410
2	426	374
3	1962	362
4	5691	362
0	8111	322

Stop Event

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

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
(*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
x
(-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)
(/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x)
#s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64)))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
y
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
(*.f64 x (-.f64 #s(literal 1/2 binary64) y))
x
(-.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
(.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
x
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
#s(literal 0 binary64)
(.f64 y (.f64 y y))
y
(*.f64 y y)
#s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
(.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))))
x
(.f64 (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(neg.f64 (.f64 y (.f64 y y)))
(.f64 y (.f64 y y))
y
(*.f64 y y)
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))
#s(literal 1 binary64)
(fma.f64 y y #s(literal 0 binary64))
#s(literal 0 binary64)
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
x
#s(approx (- 1/2 y) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

Outputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64) (neg.f64 (*.f64 x y))))
(*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
(fma.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) #s(literal 1 binary64) (neg.f64 (*.f64 x y)))
x
(-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)
(/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x)
#s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64)))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
y
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
(*.f64 x (-.f64 #s(literal 1/2 binary64) y))
x
(-.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
(.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
(/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))
x
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))
(/.f64 (neg.f64 (.f64 y (.f64 y y))) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
(neg.f64 (.f64 y (.f64 y y)))
#s(literal 0 binary64)
(.f64 y (.f64 y y))
y
(*.f64 y y)
#s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (*.f64 x y)))
(.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))))
(neg.f64 (*.f64 x y))
x
(.f64 (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(neg.f64 y)
(neg.f64 (.f64 y (.f64 y y)))
(.f64 y (.f64 y y))
y
(*.f64 y y)
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
#s(literal 1 binary64)
(fma.f64 y y #s(literal 0 binary64))
(*.f64 y y)
#s(literal 0 binary64)
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
x
#s(approx (- 1/2 y) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

localize189.0ms (2.3%)

Memory

35.2MiB live, 309.1MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
✓	accuracy	85.1%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
✓	accuracy	43.8%	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
✓	accuracy	99.9%	(.f64 y (.f64 y y))
✓	accuracy	98.5%	(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))
✓	accuracy	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
✓	accuracy	35.8%	(.f64 (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
✓	accuracy	100.0%	#s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y))
✓	accuracy	99.9%	(.f64 y (.f64 y y))
✓	accuracy	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
✓	accuracy	35.7%	(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))
✓	accuracy	100.0%	(-.f64 #s(literal 1/2 binary64) y)
✓	accuracy	100.0%	(*.f64 x (-.f64 #s(literal 1/2 binary64) y))
✓	accuracy	85.1%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
✓	accuracy	53.4%	#s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
✓	accuracy	100.0%	(-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)
✓	accuracy	99.9%	(*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
✓	accuracy	99.8%	(/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x)
✓	accuracy	64.9%	#s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64)))

Samples

99.0ms

256×

valid

Compiler

Compiled 362 to 44 computations (87.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 78.0ms

ival-log1p: 26.0ms (33.2% of total)

ival-mult: 19.0ms (24.3% of total)

ival-sub: 7.0ms (9% of total)

ival-div: 6.0ms (7.7% of total)

ival-add: 6.0ms (7.7% of total)

ival-pow: 4.0ms (5.1% of total)

ival-log: 3.0ms (3.8% of total)

ival-exp: 2.0ms (2.6% of total)

ival-pow2: 2.0ms (2.6% of total)

exact: 1.0ms (1.3% of total)

ival-neg: 1.0ms (1.3% of total)

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

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

series29.0ms (0.4%)

Memory

-17.2MiB live, 21.9MiB allocated

Counts

24 → 420

Calls

Call 1

Inputs
#<alt (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))>
#<alt #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))>
#<alt (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)>
#<alt (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x)>
#<alt #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))>
#<alt #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))>
#<alt (*.f64 x (-.f64 #s(literal 1/2 binary64) y))>
#<alt (-.f64 #s(literal 1/2 binary64) y)>
#<alt (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))>
#<alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))>
#<alt (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))>
#<alt (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))>
#<alt (.f64 (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))>
#<alt (fma.f64 y y #s(literal 0 binary64))>
#<alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))>
#<alt (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))))>
#<alt #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))>
#<alt (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))>
#<alt #s(approx (- 1/2 y) #s(literal 1/2 binary64))>
#<alt (log.f64 #s(literal 2 binary64))>
#<alt #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64)))>
#<alt (.f64 y (.f64 y y))>
#<alt #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y))>
#<alt (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))>

Outputs
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))>
#<alt (log (+ 1 (exp x)))>
#<alt (+ (log (+ 1 (exp x))) (* -1 (* x y)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))>
#<alt (* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))>
#<alt (/ (log 2) x)>
#<alt (/ (+ (log 2) (* x (- 1/2 y))) x)>
#<alt (/ (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y))) x)>
#<alt (/ (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y))) x)>
#<alt (* -1 y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (* -1 y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (- (/ (log (+ 1 (exp x))) x) y)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (+ (* -1 y) (/ (log (+ 1 (exp x))) x))>
#<alt (+ (* -1 y) (/ (log (+ 1 (exp x))) x))>
#<alt (+ (* -1 y) (/ (log (+ 1 (exp x))) x))>
#<alt (* -1 y)>
#<alt (* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))>
#<alt (* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))>
#<alt (* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))>
#<alt (/ (log 2) x)>
#<alt (/ (+ (log 2) (* 1/2 x)) x)>
#<alt (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) x)>
#<alt (/ (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (/ (log (+ 1 (exp x))) x)>
#<alt (log 2)>
#<alt (+ (log 2) (* x (- 1/2 y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))>
#<alt (* -1 (* x y))>
#<alt (* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))>
#<alt (* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))>
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#<alt (log (+ 1 (exp x)))>
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#<alt (log 2)>
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#<alt (* -1 (* x y))>
#<alt (* -1 y)>
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#<alt (pow y 2)>
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#<alt (log 2)>
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#<alt (* -1 (* x y))>
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#<alt 1/2>
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#<alt (* -1 y)>
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#<alt (log 2)>
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#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (log (+ 1 (exp x)))>
#<alt (pow y 3)>
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#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>
#<alt (/ 1 (pow y 2))>

Calls

105 calls:

Time	Variable		Point	Expression
20.0ms	y	@	-inf	(* x (- (/ (log (+ 1 (exp x))) x) y))
0.0ms	x	@	inf	(* x (- 1/2 y))
0.0ms	x	@	0	(* x (- 1/2 y))
0.0ms	y	@	inf	(- (/ (log (+ 1 (exp x))) x) y)
0.0ms	x	@	0	(/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2))))

simplify338.0ms (4.1%)

Memory

15.2MiB live, 642.2MiB allocated

Algorithm

1×	egg-herbie

Rules

9 786×	`lower-fma.f64`
9 786×	`lower-fma.f32`
4 584×	`lower-+.f64`
4 584×	`lower-+.f32`
4 078×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	290	4025
1	971	3779
2	3478	3614
0	9139	3218

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))
(/ (log 2) x)
(/ (+ (log 2) (* x (- 1/2 y))) x)
(/ (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y))) x)
(/ (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y))) x)
(* -1 y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(* -1 y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(/ (log (+ 1 (exp x))) x)
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(* -1 y)
(* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))
(* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))
(* y (- (/ (log (+ 1 (exp x))) (* x y)) 1))
(* -1 y)
(* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))
(* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))
(* -1 (* y (+ 1 (* -1 (/ (log (+ 1 (exp x))) (* x y))))))
(/ (log 2) x)
(/ (+ (log 2) (* 1/2 x)) x)
(/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) x)
(/ (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(/ (log (+ 1 (exp x))) x)
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- 1/2 y)))
(* x (- 1/2 y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- 1/2 y))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(+ (log 2) (* 1/2 x))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(* -1 (* x y))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* x (- 1/2 y))
(* 1/2 x)
(+ (* -1 (* x y)) (* 1/2 x))
(+ (* -1 (* x y)) (* 1/2 x))
(+ (* -1 (* x y)) (* 1/2 x))
(* -1 (* x y))
(* y (+ (* -1 x) (* 1/2 (/ x y))))
(* y (+ (* -1 x) (* 1/2 (/ x y))))
(* y (+ (* -1 x) (* 1/2 (/ x y))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1/2 (/ x y)))))
(* -1 (* y (+ x (* -1/2 (/ x y)))))
(* -1 (* y (+ x (* -1/2 (/ x y)))))
1/2
(+ 1/2 (* -1 y))
(+ 1/2 (* -1 y))
(+ 1/2 (* -1 y))
(* -1 y)
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* -1 y)
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(* -1 (pow y 3))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(* -1 y)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(* -1 (* x y))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(* -1 (* x y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))
(* -1 (* x y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))
(* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(* -1 (* x y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- 1/2 y)))
(* x (- 1/2 y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* x (- 1/2 y))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(+ (log 2) (* 1/2 x))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(* -1 (* x y))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* -1 (* x y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
1/2
(+ 1/2 (* -1 y))
(+ 1/2 (* -1 y))
(+ 1/2 (* -1 y))
(* -1 y)
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* -1 y)
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(log 2)
(+ (log 2) (* 1/2 x))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(log (+ 1 (exp x)))
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 3)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(pow y 2)
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))
(/ 1 (pow y 2))

Outputs
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* x (- 1/2 y)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64)))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* x (- 1/2 y)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(fma.f64 x (fma.f64 x (-.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))) #s(literal -3/8 binary64))) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (.f64 (+.f64 y #s(literal 1 binary64)) (/.f64 y (log.f64 #s(literal 2 binary64)))))) (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (- (+ 1/2 (* x (- (+ (* 1/4 (/ 1 (log 2))) (+ (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2))) (* x (- (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (pow (log 2) 2))) (+ (/ (* (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2))) (+ 1/2 y)) (pow (log 2) 2)) (+ (/ (* (+ (* 1/8 (pow (log 2) 2)) (+ (* (log 2) (+ 1/4 (+ (* 1/4 (log 2)) (pow y 2)))) (* (log 2) (+ 1/2 y)))) (- 1/2 y)) (pow (log 2) 3)) (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- (+ (* 1/4 (/ 1 (log 2))) (* 2 (/ (+ 1/4 (* 1/4 (log 2))) (log 2)))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2))))))) (pow (log 2) 3)))))))) (+ 3/8 (+ (/ y (log 2)) (+ (/ (* (+ (* (pow (log 2) 2) (+ 1/2 y)) (pow (log 2) 2)) (- 1/2 y)) (pow (log 2) 3)) (/ (pow y 2) (log 2)))))))) y)))
(fma.f64 x (-.f64 (fma.f64 x (+.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64)))) (fma.f64 x (-.f64 (/.f64 (fma.f64 #s(literal 2 binary64) (.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (fma.f64 (-.f64 (fma.f64 #s(literal 2 binary64) (/.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) #s(literal 1/4 binary64)) (log.f64 #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 2 binary64))) #s(literal -3/8 binary64))) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (.f64 (+.f64 y #s(literal 1 binary64)) (/.f64 y (log.f64 #s(literal 2 binary64)))))) (/.f64 (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (fma.f64 (+.f64 #s(literal 1/2 binary64) y) (/.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (fma.f64 y y #s(literal 1/4 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (.f64 (.f64 (log.f64 #s(literal 2 binary64)) (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/8 binary64) (+.f64 (fma.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/4 binary64) (.f64 y y)) (+.f64 #s(literal 3/4 binary64) y)))) (/.f64 (-.f64 #s(literal 1/2 binary64) y) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))))))) (-.f64 #s(literal -3/8 binary64) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) (/.f64 (.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64))) (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 3 binary64))) (*.f64 (+.f64 y #s(literal 1 binary64)) (/.f64 y (log.f64 #s(literal 2 binary64)))))))) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* x (+ (* -1 y) (/ (log (+ 1 (exp x))) x)))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y)) (pow x 2)))) (* -1 (/ (log (+ 1 (exp x))) x))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* x (- (+ (* -1 y) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow y 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow y 2)))) (pow x 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))) (/ (pow (log (+ 1 (exp x))) 2) (* (pow x 2) y))))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (+ y (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) x)))))
(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
(* -1 (* x (+ y (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2)))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 2))))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) y)) (/ (pow (log (+ 1 (exp x))) 2) y))) x)) (* -1 (log (+ 1 (exp x))))) x)))))
(.f64 x (+.f64 (/.f64 (+.f64 (log1p.f64 (exp.f64 x)) (/.f64 (.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 3 binary64)) (.f64 x (.f64 y y)))) x)) x) (neg.f64 y)))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* y (- (* -1 (* y (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(+ (log (+ 1 (exp x))) (* y (- (* y (- (* -1 (* y (+ (* -1 (/ (* x (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x)))))) (log (+ 1 (exp x))))) (+ (* -1 (/ (pow x 3) (pow (log (+ 1 (exp x))) 2))) (/ (pow x 3) (pow (log (+ 1 (exp x))) 2)))))) (+ (* -1 (/ (pow x 2) (log (+ 1 (exp x))))) (/ (pow x 2) (log (+ 1 (exp x))))))) x)))
(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* y (+ (* -1 x) (/ (log (+ 1 (exp x))) y)))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x)) (pow y 2)))) (* -1 (/ (log (+ 1 (exp x))) y))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* y (- (+ (* -1 x) (* -1 (/ (+ (* -1 (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) x)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (pow x 2))) (/ (pow (log (+ 1 (exp x))) 3) (pow x 2)))) (pow y 3)))) (+ (* -1 (/ (log (+ 1 (exp x))) y)) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))) (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 2)))))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* y (+ x (* -1 (/ (log (+ 1 (exp x))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (+ x (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (/ (pow (log (+ 1 (exp x))) 2) (* x y))) (* -1 (log (+ 1 (exp x))))) y)))))
(*.f64 y (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) y) x))
(* -1 (* y (+ x (* -1 (/ (- (* -1 (/ (- (+ (* -1 (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y))) (+ (/ (* (log (+ 1 (exp x))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) (* x y)) (/ (pow (log (+ 1 (exp x))) 3) (* (pow x 2) y)))) (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) x)) (/ (pow (log (+ 1 (exp x))) 2) x))) y)) (* -1 (log (+ 1 (exp x))))) y)))))
(.f64 (+.f64 x (/.f64 (-.f64 (/.f64 (.f64 #s(literal 0 binary64) (/.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 3 binary64)) (.f64 y (.f64 x x)))) y) (log1p.f64 (exp.f64 x))) y)) (neg.f64 y))
(/ (log 2) x)
(/.f64 (log.f64 #s(literal 2 binary64)) x)
(/ (+ (log 2) (* x (- 1/2 y))) x)
(/.f64 (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))) x)
(/ (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y))) x)
(/.f64 (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))) x)
(/ (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y))) x)
(/.f64 (fma.f64 x (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) (-.f64 #s(literal 1/2 binary64) y)) (log.f64 #s(literal 2 binary64))) x)
(* -1 y)
(neg.f64 y)
(- (/ (log (+ 1 (exp x))) x) y)
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(* -1 y)
(neg.f64 y)
(- (/ (log (+ 1 (exp x))) x) y)
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(- (/ (log (+ 1 (exp x))) x) y)
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(/ (log (+ 1 (exp x))) x)
(/.f64 (log1p.f64 (exp.f64 x)) x)
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(+ (* -1 y) (/ (log (+ 1 (exp x))) x))
(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
(* -1 y)
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(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(*.f64 x (+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (log.f64 #s(literal 2 binary64)) x) y)))
(+ (log 2) (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(*.f64 y (-.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) x))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(*.f64 y (-.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) x))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(*.f64 y (-.f64 (fma.f64 x (/.f64 #s(literal 1/2 binary64) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) x))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(*.f64 (-.f64 x (/.f64 (fma.f64 x #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(*.f64 (-.f64 x (/.f64 (fma.f64 x #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(*.f64 (-.f64 x (/.f64 (fma.f64 x #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1 y))
(-.f64 #s(literal 1/2 binary64) y)
(+ 1/2 (* -1 y))
(-.f64 #s(literal 1/2 binary64) y)
(+ 1/2 (* -1 y))
(-.f64 #s(literal 1/2 binary64) y)
(* -1 y)
(neg.f64 y)
(* y (- (* 1/2 (/ 1 y)) 1))
(-.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) y)) y)
(* y (- (* 1/2 (/ 1 y)) 1))
(-.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) y)) y)
(* y (- (* 1/2 (/ 1 y)) 1))
(-.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) y)) y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(-.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) y)) y)
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(-.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) y)) y)
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(-.f64 (*.f64 y (/.f64 #s(literal 1/2 binary64) y)) y)
(log 2)
(log.f64 #s(literal 2 binary64))
(+ (log 2) (* 1/2 x))
(fma.f64 x #s(literal 1/2 binary64) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))
(fma.f64 x (fma.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(log (+ 1 (exp x)))
(log1p.f64 (exp.f64 x))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 3)
(.f64 y (.f64 y y))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))
(/ 1 (pow y 2))
(/.f64 #s(literal 1 binary64) (*.f64 y y))

rewrite360.0ms (4.3%)

Memory

-0.3MiB live, 619.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 182×	`lower-*.f32`
5 174×	`lower-fma.f32`
5 170×	`lower-fma.f64`
5 168×	`lower-*.f64`
3 120×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	434
0	76	379
1	348	239
2	2803	239
0	8350	217

Stop Event

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

Counts

24 → 760

Calls

Call 1

Inputs
(*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
(-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)
(/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x)
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y)))
(*.f64 x (-.f64 #s(literal 1/2 binary64) y))
(-.f64 #s(literal 1/2 binary64) y)
(-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
(.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))
(.f64 (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))
(fma.f64 y y #s(literal 0 binary64))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
(.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))
#s(approx (- 1/2 y) #s(literal 1/2 binary64))
(log.f64 #s(literal 2 binary64))
#s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64)))
(.f64 y (.f64 y y))
#s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y))
(/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64)))

Outputs
(+.f64 (.f64 x (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x)) (.f64 x (neg.f64 y)))
(+.f64 (.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) x) (.f64 x (neg.f64 y)))
(fma.f64 x (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) (*.f64 x (neg.f64 y)))
(fma.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) x (*.f64 x (neg.f64 y)))
(/.f64 (.f64 x (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y)))) (fma.f64 y (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y))) (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y))) x) (fma.f64 y (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y)) x) (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
(*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
(*.f64 (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) x)
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
(+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) (neg.f64 y))
(+.f64 (neg.f64 y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)
(-.f64 (/.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) (fma.f64 y (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 y (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)) (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)) (/.f64 (*.f64 y y) (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) (neg.f64 y))
(fma.f64 #s(literal 1 binary64) (neg.f64 y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) x) (neg.f64 y))
(fma.f64 y (.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal 1 binary64) (*.f64 y y))) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 y (/.f64 (neg.f64 (.f64 y y)) (.f64 y y)) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (.f64 y (.f64 y y)) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y))) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 y y)) (neg.f64 (.f64 y (*.f64 y y))) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 #s(literal -1 binary64) y (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (neg.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 y))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) (neg.f64 y))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64)))) #s(literal -1 binary64)) (neg.f64 y))
(fma.f64 (neg.f64 y) #s(literal 1 binary64) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 y y) (/.f64 (neg.f64 (*.f64 y y)) y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 #s(literal -1 binary64) y) (/.f64 (.f64 y (.f64 y y)) y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 (neg.f64 y) y) (/.f64 (*.f64 y y) y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) y) (/.f64 #s(literal 1 binary64) y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 y y)) #s(literal -1 binary64)) (.f64 y (.f64 y y)) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 y y)) (neg.f64 y)) (*.f64 y y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(fma.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (neg.f64 (.f64 y (.f64 y (.f64 y y))))) (neg.f64 (.f64 y y)) (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64))) (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y))) (fma.f64 y (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y))) (+.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)) (-.f64 (.f64 y y) (.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) (neg.f64 y)))))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y)) (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y))
(/.f64 (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y)) (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) (neg.f64 y)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y)))) (neg.f64 (fma.f64 y (+.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
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(/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))
(/.f64 #s(literal -1 binary64) (neg.f64 (*.f64 y y)))
(/.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))
(/.f64 (/.f64 #s(literal 1 binary64) y) y)
(pow.f64 y #s(literal -2 binary64))
(pow.f64 (*.f64 y y) #s(literal -1 binary64))
(pow.f64 (.f64 y (.f64 y (*.f64 y y))) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) y) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 (*.f64 y y))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 y y)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y y)) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 y y))))
(*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y))
(*.f64 (/.f64 #s(literal 1 binary64) y) (pow.f64 (/.f64 y #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (.f64 y (.f64 y (*.f64 y y))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 y y)) #s(literal -2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))))) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y (*.f64 y y)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y (.f64 y y)))) (*.f64 y y))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 y (.f64 y (.f64 y y)))) (pow.f64 (.f64 y (/.f64 #s(literal 1 binary64) (.f64 y y))) #s(literal -2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 y (.f64 y (.f64 y y))))) (neg.f64 (*.f64 y y)))
(.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (.f64 y (.f64 y (.f64 y y))))) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 y y))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 y y)) #s(literal -2 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y y) (.f64 y (.f64 y (*.f64 y y))))))

eval194.0ms (2.3%)

Memory: 3.1MiB live, 339.5MiB allocated
Compiler: Compiled 29 588 to 2 927 computations (90.1% saved)

prune144.0ms (1.7%)

Memory

-8.6MiB live, 386.9MiB allocated

Pruning

25 alts after pruning (16 fresh and 9 done)

	Pruned	Kept	Total
New	1 239	13	1 252
Fresh	1	3	4
Picked	2	3	5
Done	0	6	6
Total	1 242	25	1 267

Accuracy

99.7%

Counts

1 267 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	77.0%	(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
✓	93.5%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
✓	85.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
✓	48.2%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
	10.5%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
✓	93.4%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
	48.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
	21.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
✓	39.1%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
	85.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (log.f64 #s(literal 2 binary64)) x) y)))))
	3.5%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
	39.0%	#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
✓	78.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
	10.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
	12.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
	13.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
	7.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
	8.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
	28.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
	8.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
	8.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))
	14.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
✓	53.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
	21.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
✓	8.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))

Compiler

Compiled 926 to 332 computations (64.1% saved)

regimes38.0ms (0.5%)

Memory

-22.4MiB live, 73.9MiB allocated

Counts

38 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (log.f64 #s(literal 2 binary64)) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (*.f64 y (+.f64 (neg.f64 x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))) y)))))
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
(-.f64 (neg.f64 (log.f64 (/.f64 #s(approx (- (exp x) 1) (fma.f64 (.f64 x x) (fma.f64 x #s(literal 1/6 binary64) #s(literal 1/2 binary64)) x)) (expm1.f64 (+.f64 x x))))) (.f64 x y))
(-.f64 (neg.f64 (log.f64 (/.f64 (expm1.f64 x) (expm1.f64 (+.f64 x x))))) (*.f64 x y))
(/.f64 (fma.f64 x (.f64 y (.f64 x (.f64 x (.f64 y y)))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 3 binary64))) (fma.f64 (*.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 4 binary64)) (.f64 x (.f64 (.f64 x (.f64 y y)) (.f64 x (.f64 x (.f64 y y)))))) (.f64 (fma.f64 x y (log1p.f64 (exp.f64 x))) (fma.f64 x (.f64 x (.f64 y y)) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)))))
(.f64 (fma.f64 (.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))) (.f64 (-.f64 (log1p.f64 (exp.f64 x)) (.f64 x y)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) (fma.f64 x y (log1p.f64 (exp.f64 x))) (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64))))))

Outputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Calls

3 calls:

15.0ms	y
10.0ms	x
10.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`y`
99.6%	1	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes29.0ms (0.3%)

Memory

29.8MiB live, 68.7MiB allocated

Counts

31 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (*.f64 x (-.f64 (/.f64 #s(approx (log (+ 1 (exp x))) (log.f64 #s(literal 2 binary64))) x) y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (+.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (log.f64 #s(literal 2 binary64)) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (*.f64 y (+.f64 (neg.f64 x) (/.f64 (fma.f64 x (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))) y)))))

Outputs

#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))

#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64))))

Calls

3 calls:

10.0ms	y
9.0ms	x
8.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
99.6%	2	`x`
93.5%	1	`y`
98.9%	2	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes10.0ms (0.1%)

Memory

-18.5MiB live, 19.8MiB allocated

Counts

27 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))

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

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
99.6%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes9.0ms (0.1%)

Memory

18.5MiB live, 18.5MiB allocated

Counts

25 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes27.0ms (0.3%)

Memory

-15.1MiB live, 26.2MiB allocated

Counts

24 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))

Outputs

#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))

#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64))))

#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))

Calls

2 calls:

19.0ms	x
6.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
97.8%	3	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
83.0%	2	`x`

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes8.0ms (0.1%)

Memory

14.4MiB live, 14.4MiB allocated

Counts

23 → 3

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (log.f64 #s(literal 2 binary64)))

Outputs

#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))

#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))

#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))

Calls

1 calls:

6.0ms

(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
97.6%	3	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes35.0ms (0.4%)

Memory

4.4MiB live, 42.4MiB allocated

Counts

21 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x (-.f64 #s(literal 1/2 binary64) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) #s(approx (* x (- 1/2 y)) (.f64 y (-.f64 (/.f64 (.f64 x #s(literal 1/2 binary64)) y) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* x (- (+ (* x 1/8) 1/2) y)) (log 2)) (.f64 (.f64 x x) (+.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 y #s(literal 1/2 binary64)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 #s(literal 1 binary64) y) (neg.f64 (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 (/.f64 (.f64 y (.f64 y y)) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))) x))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (/.f64 (neg.f64 (.f64 x (.f64 y (.f64 y y)))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) #s(approx (+ 0 (+ ( y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 (.f64 x (neg.f64 (.f64 y (*.f64 y y)))) (fma.f64 y y #s(literal 0 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 x (/.f64 #s(literal 1 binary64) (.f64 y y))) (neg.f64 (.f64 y (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 y y #s(literal 0 binary64))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (+.f64 #s(literal 0 binary64) (fma.f64 y y (.f64 #s(literal 0 binary64) y))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 0 (+ (* y y) (* 0 y))) (.f64 y y)) (neg.f64 (.f64 x (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (*.f64 (/.f64 #s(literal 1 binary64) y) (/.f64 #s(literal 1 binary64) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (/.f64 (neg.f64 (.f64 y (.f64 y y))) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (/.f64 (/.f64 (.f64 (neg.f64 y) (.f64 y (.f64 y (.f64 y y)))) (.f64 y y)) #s(approx (+ 0 (+ (* y y) (* 0 y))) (*.f64 y y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (.f64 (neg.f64 (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 y (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (*.f64 y y)))))))

Outputs
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))

Calls

3 calls:

21.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
6.0ms	y
6.0ms	x

Results

Accuracy	Segments	Branch
53.4%	1	`x`
53.4%	1	`y`
53.4%	1	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes6.0ms (0.1%)

Memory

-25.3MiB live, 12.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs

#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))

Outputs

#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))

Calls

3 calls:

3.0ms	x
1.0ms	y
1.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
3.5%	1	`x`
3.5%	1	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
3.5%	1	`y`

Compiler

Compiled 17 to 12 computations (29.4% saved)

bsearch16.0ms (0.2%)

Memory

0.6MiB live, 37.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	-458009.32215004327	-0.00016684909911796015

Samples

7.0ms

144×

valid

Compiler

Compiled 212 to 146 computations (31.1% saved)

Precisions

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

ival-exp: 2.0ms (45.8% of total)

ival-sub: 1.0ms (22.9% of total)

ival-log1p: 1.0ms (22.9% of total)

ival-mult: 1.0ms (22.9% of total)

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

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

bsearch13.0ms (0.2%)

Memory

34.9MiB live, 34.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	-458009.32215004327	-0.00016684909911796015

Samples

7.0ms

128×

valid

Compiler

Compiled 185 to 128 computations (30.8% saved)

Precisions

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

ival-log1p: 2.0ms (43.2% of total)

ival-sub: 1.0ms (21.6% of total)

ival-exp: 1.0ms (21.6% of total)

ival-mult: 1.0ms (21.6% of total)

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

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

bsearch1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-458009.32215004327	-0.00016684909911796015

Compiler

Compiled 176 to 119 computations (32.4% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.6936151813635473	472.4254465396472
0.0ms	1.1280591985167118e-5	0.6930617062782565

Compiler

Compiled 14 to 13 computations (7.1% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.6936151813635473	472.4254465396472
0.0ms	1.1280591985167118e-5	0.6930617062782565

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify12.0ms (0.1%)

Memory

-19.6MiB live, 24.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
14×	`sub-neg_binary64`
12×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	68	366
1	88	366
2	99	366
3	104	366
4	106	366

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(if (<=.f64 x #s(literal -145 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (neg.f64 y))) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -3152519739159347/2251799813685248 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (neg.f64 y))) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -145 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (neg.f64 y))) (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 5902958103587057/295147905179352825856 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 x (neg.f64 y))) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 5902958103587057/295147905179352825856 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 x (neg.f64 y))) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))

Outputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(if (<=.f64 x #s(literal -145 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (neg.f64 y))) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -145 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (.f64 x y))) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 x (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y) (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -3152519739159347/2251799813685248 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (neg.f64 y))) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -3152519739159347/2251799813685248 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (.f64 x y))) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -145 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 x (neg.f64 y))) (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)))
(if (<=.f64 x #s(literal -145 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (.f64 x y))) (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 5902958103587057/295147905179352825856 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 x (neg.f64 y))) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 5902958103587057/295147905179352825856 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (neg.f64 (.f64 x y))) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) (fma.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (log.f64 #s(literal 2 binary64)))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (*.f64 x y)))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 5902958103587057/295147905179352825856 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 x (neg.f64 y))) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 5902958103587057/295147905179352825856 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (neg.f64 (.f64 x y))) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (*.f64 x y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (*.f64 x y)))
#s(approx (/ (- (pow (log (+ 1 (exp x))) 4) (* x (* (* x (* y y)) (* x (* x (* y y)))))) (* (+ (* x y) (log (+ 1 (exp x)))) (+ (* x (* x (* y y))) (pow (log (+ 1 (exp x))) 2)))) #s(approx (+ (* x (- 1/2 y)) (log 2)) (*.f64 x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))))

soundness1.3s (16%)

Memory

-17.3MiB live, 659.9MiB allocated

Rules

11 474×	`lower-fma.f64`
11 474×	`lower-fma.f32`
9 786×	`lower-fma.f64`
9 786×	`lower-fma.f32`
7 786×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	416	4067
1	1314	3963
2	4317	3889
0	8436	3346
0	67	400
1	180	400
2	389	400
3	1353	400
4	4014	370
5	6856	370
0	8132	300
0	8	20
0	13	20
1	47	20
2	311	20
3	2718	20
0	9051	16
0	290	4025
1	971	3779
2	3478	3614
0	9139	3218
0	395	3915
1	1245	3742
2	4112	3632
0	8371	3079

Stop Event

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

Compiler

Compiled 279 to 127 computations (54.5% saved)

preprocess152.0ms (1.8%)

Memory: 17.1MiB live, 135.3MiB allocated
Compiler: Compiled 384 to 122 computations (68.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	22	51
1	58	49
2	113	49
3	227	49
4	311	49
5	429	49
6	483	49
7	515	49
8	518	49
0	8	9
0	13	9
1	22	9
2	33	9
3	45	9
4	60	9
5	84	9
6	123	9
7	160	9
8	205	9
9	231	9
10	255	9
11	264	9
0	264	7

Iter	Nodes	Cost
0	8	26
0	13	26
1	22	26
2	33	26
3	45	26
4	60	26
5	84	26
6	123	26
7	160	26
8	205	26
9	231	26
10	255	26
11	264	26
0	264	22

Iter	Nodes	Cost
0	22	51
1	58	49
2	113	49
3	227	49
4	311	49
5	429	49
6	483	49
7	515	49
8	518	49
0	8	9
0	13	9
1	22	9
2	33	9
3	45	9
4	60	9
5	84	9
6	123	9
7	160	9
8	205	9
9	231	9
10	255	9
11	264	9
0	264	7

Iter	Nodes	Cost
0	8	26
0	13	26
1	22	26
2	33	26
3	45	26
4	60	26
5	84	26
6	123	26
7	160	26
8	205	26
9	231	26
10	255	26
11	264	26
0	264	22

analyze71.0ms (0.8%)

sample1.0s (12.1%)

preprocess34.0ms (0.4%)

explain105.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify13.0ms (0.2%)

localize27.0ms (0.3%)

series55.0ms (0.7%)

simplify261.0ms (3.1%)

rewrite413.0ms (5%)

eval55.0ms (0.7%)

prune134.0ms (1.6%)

simplify279.0ms (3.4%)

localize184.0ms (2.2%)

series110.0ms (1.3%)

simplify335.0ms (4%)

rewrite455.0ms (5.5%)

eval204.0ms (2.5%)

prune187.0ms (2.2%)

simplify302.0ms (3.6%)

localize191.0ms (2.3%)

series30.0ms (0.4%)

simplify406.0ms (4.9%)

rewrite60.0ms (0.7%)

eval85.0ms (1%)

prune73.0ms (0.9%)

simplify287.0ms (3.5%)

localize189.0ms (2.3%)

series29.0ms (0.4%)

simplify338.0ms (4.1%)

rewrite360.0ms (4.3%)

eval194.0ms (2.3%)

prune144.0ms (1.7%)

regimes38.0ms (0.5%)

regimes29.0ms (0.3%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes27.0ms (0.3%)

regimes8.0ms (0.1%)

regimes35.0ms (0.4%)

regimes6.0ms (0.1%)

bsearch16.0ms (0.2%)

bsearch13.0ms (0.2%)

bsearch1.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify12.0ms (0.1%)

soundness1.3s (16%)

preprocess152.0ms (1.8%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	22	51
1	58	49
2	113	49
3	227	49
4	311	49
5	429	49
6	483	49
7	515	49
8	518	49
0	8	9
0	13	9
1	22	9
2	33	9
3	45	9
4	60	9
5	84	9
6	123	9
7	160	9
8	205	9
9	231	9
10	255	9
11	264	9
0	264	7

Iter	Nodes	Cost
0	8	26
0	13	26
1	22	26
2	33	26
3	45	26
4	60	26
5	84	26
6	123	26
7	160	26
8	205	26
9	231	26
10	255	26
11	264	26
0	264	22