Metrics for Logistic regression 2

analyze71.0ms (1%)

Memory

20.7MiB live, 130.7MiB 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)

sample1.4s (19.1%)

Memory

36.6MiB live, 1 500.4MiB allocated

Samples

796.0ms	8 256×	0	valid
233.0ms	2 615×	1	exit

Precisions

Click to see histograms. Total time spent on operations: 435.0ms

ival-log1p: 124.0ms (28.5% of total)

ival-mult: 116.0ms (26.7% of total)

ival-exp: 95.0ms (21.8% of total)

ival-sub: 52.0ms (12% of total)

adjust: 34.0ms (7.8% of total)

ival-true: 8.0ms (1.8% of total)

ival-assert: 5.0ms (1.1% of total)

Bogosity

preprocess34.0ms (0.5%)

Memory

7.0MiB live, 43.3MiB 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))

explain145.0ms (2%)

Memory

-13.7MiB live, 145.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
6	83	(-7.089200354973112e+68 4.125910514518026e+62)	-	`(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	84	0
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`	oflow-rescue	5	0
↳	`(exp.f64 x)`	overflow	5
↳	`(+.f64 #s(literal 1 binary64) (exp.f64 x))`	overflow	5

Confusion

	Predicted +	Predicted -
+	5	0
-	84	167

Precision

0.056179775280898875

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	5	0	0
-	84	0	167

Precision?

0.056179775280898875

Recall?

1.0

Freqs

test

number	freq
0	167
1	89

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

80.0ms

512×

valid

Compiler

Compiled 78 to 36 computations (53.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-add: 28.0ms (61.7% of total)

ival-log1p: 6.0ms (13.2% of total)

ival-exp: 4.0ms (8.8% of total)

ival-mult: 4.0ms (8.8% of total)

ival-sub: 2.0ms (4.4% 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: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.1%	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify15.0ms (0.2%)

Memory

-14.0MiB live, 23.5MiB 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

localize37.0ms (0.5%)

Memory

0.5MiB live, 38.3MiB 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	97.7%	(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Samples

17.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-log1p: 3.0ms (31.3% of total)

ival-exp: 2.0ms (20.9% of total)

ival-mult: 2.0ms (20.9% of total)

ival-sub: 1.0ms (10.4% of total)

ival-add: 1.0ms (10.4% of total)

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

exact: 0.0ms (0% of total)

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

series65.0ms (0.9%)

Memory

-2.5MiB live, 50.0MiB 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
32.0ms	x	@	-inf	(log (+ 1 (exp x)))
27.0ms	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))

simplify287.0ms (3.9%)

Memory

14.5MiB live, 400.6MiB 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)

rewrite372.0ms (5.1%)

Memory

6.0MiB live, 589.6MiB 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))

eval53.0ms (0.7%)

Memory: 13.3MiB live, 129.2MiB allocated
Compiler: Compiled 15 047 to 1 438 computations (90.4% saved)

prune54.0ms (0.7%)

Memory

24.8MiB live, 140.9MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	411	8	419
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	412	8	420

Accuracy

99.7%

Counts

420 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.6%	(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))
▶	91.5%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
	73.8%	#s(approx (- (log (+ 1 (exp x))) (* x 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))))
▶	75.4%	#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))))
	82.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
▶	53.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
▶	48.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))
	47.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))

Compiler

Compiled 150 to 110 computations (26.7% saved)

simplify483.0ms (6.6%)

Memory

-16.6MiB live, 727.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	192	(log1p.f64 (exp.f64 x))
✓	cost-diff	6208	(exp.f64 x)
✓	cost-diff	0	(log.f64 #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	(*.f64 x y)
✓	cost-diff	0	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
✓	cost-diff	6464	(-.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	1792	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓	cost-diff	5888	(expm1.f64 (+.f64 x x))
✓	cost-diff	6016	(expm1.f64 x)
✓	cost-diff	6464	(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))

Rules

12 174×	`lower-fma.f32`
12 170×	`lower-fma.f64`
2 238×	`lower-*.f32`
2 234×	`lower-*.f64`
2 186×	`lower-+.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	123
0	54	156
1	85	156
2	125	156
3	225	146
4	390	110
5	617	110
6	1247	110
7	3596	110
8	7629	110
0	8157	110

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
x
(expm1.f64 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)
#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(exp.f64 x)
x

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

localize143.0ms (1.9%)

Memory

-15.2MiB live, 216.3MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(exp.f64 x)
✓	accuracy	98.1%	(log1p.f64 (exp.f64 x))
✓	accuracy	100.0%	(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
✓	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	100.0%	(*.f64 x y)
✓	accuracy	100.0%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
✓	accuracy	97.7%	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(*.f64 x (neg.f64 y))
✓	accuracy	100.0%	(neg.f64 y)
✓	accuracy	100.0%	(expm1.f64 x)
✓	accuracy	100.0%	(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))
✓	accuracy	98.0%	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓	accuracy	97.7%	(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

Samples

64.0ms	66×	2	valid
32.0ms	172×	0	valid
9.0ms	18×	1	valid

Compiler

Compiled 157 to 27 computations (82.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 84.0ms

ival-log: 41.0ms (48.8% of total)

ival-mult: 8.0ms (9.5% of total)

ival-add: 7.0ms (8.3% of total)

adjust: 7.0ms (8.3% of total)

ival-expm1: 5.0ms (5.9% of total)

ival-sub: 5.0ms (5.9% of total)

ival-div: 3.0ms (3.6% of total)

ival-exp: 3.0ms (3.6% of total)

ival-log1p: 3.0ms (3.6% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

exact: 0.0ms (0% of total)

series98.0ms (1.3%)

Memory

-7.9MiB live, 72.5MiB allocated

Counts

16 → 252

Calls

Call 1

Inputs
#<alt (-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))>
#<alt (expm1.f64 x)>
#<alt (expm1.f64 (+.f64 x x))>
#<alt (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))>
#<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 (*.f64 x y)>
#<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 (log.f64 #s(literal 2 binary64))>
#<alt (exp.f64 x)>
#<alt (log1p.f64 (exp.f64 x))>
#<alt (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 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 (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))>
#<alt (* x (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))>
#<alt (* x (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))>
#<alt (* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))>
#<alt (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))>
#<alt (+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))>
#<alt (+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))>
#<alt (* -1 (* x y))>
#<alt (* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))>
#<alt (* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))>
#<alt (* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (- (* -1 (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y)) (* -1 x))))>
#<alt (* -1 (* y (- (* -1 (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y)) (* -1 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 (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<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 (* 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 (* 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 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)>
#<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) (* 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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>

Calls

63 calls:

Time	Variable		Point	Expression
48.0ms	x	@	inf	(log (/ (- (exp (+ x x)) 1) (- (exp x) 1)))
28.0ms	x	@	-inf	(log (/ (- (exp (+ x x)) 1) (- (exp x) 1)))
4.0ms	y	@	0	(- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y))
3.0ms	x	@	inf	(- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y))
3.0ms	x	@	-inf	(- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y))

simplify439.0ms (6%)

Memory

9.6MiB live, 362.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 240×	`lower-fma.f64`
12 240×	`lower-fma.f32`
4 182×	`lower-*.f64`
4 182×	`lower-*.f32`
2 360×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	173	1841
1	517	1824
2	1310	1824
3	5093	1806
0	8233	1475

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 251

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 (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))
(* x (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))
(* x (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))
(* -1 (* x y))
(* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))
(* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))
(+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))
(+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))
(* -1 (* x y))
(* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))
(* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))
(* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))
(* -1 (* x y))
(* -1 (* y (- (* -1 (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y)) (* -1 x))))
(* -1 (* y (- (* -1 (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y)) (* -1 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)
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (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) (- (exp x) 1))
(* -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)))
(* 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 (* 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))))
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)
(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) (* 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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 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 (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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) x) y))
(* x (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) x) y))
(* x (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) x) y))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) x) y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) x) y))
(* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) x) y))
(* -1 (* x (- (* -1 (/ (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))) x)) (* -1 y))))
(*.f64 x (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) x) y))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))
(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))
(+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))
(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))
(+ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) (* -1 (* x y)))
(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) y) x))
(* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) y) x))
(* y (- (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y) x))
(*.f64 y (-.f64 (/.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) y) x))
(* -1 (* x y))
(*.f64 x (neg.f64 y))
(* -1 (* y (- (* -1 (/ (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1))) y)) (* -1 x))))
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(+ (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 #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) (* 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 #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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

rewrite128.0ms (1.7%)

Memory

22.5MiB live, 98.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

642×	`lower-fma.f32`
638×	`lower-fma.f64`
608×	`lower-*.f32`
604×	`lower-*.f64`
510×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	26	79
0	47	79
1	182	66
0	1414	66

Stop Event

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

Counts

16 → 250

Calls

Call 1

Inputs
(-.f64 (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))) (*.f64 x y))
(expm1.f64 x)
(expm1.f64 (+.f64 x x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(*.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)))
(*.f64 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)))
(-.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))
(log.f64 #s(literal 2 binary64))
(exp.f64 x)
(log1p.f64 (exp.f64 x))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

Outputs
(+.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (neg.f64 (*.f64 x y)))
(+.f64 (neg.f64 (*.f64 x y)) (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
(-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (-.f64 (log.f64 (expm1.f64 x)) (neg.f64 (*.f64 x y))))
(-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (+.f64 (log.f64 (expm1.f64 x)) (*.f64 x y)))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 3 binary64)) (fma.f64 (.f64 x y) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)))) (/.f64 (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))) (fma.f64 (*.f64 x y) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))) (/.f64 (.f64 x (.f64 y (*.f64 x y))) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))))
(fma.f64 x (neg.f64 y) (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(fma.f64 y (neg.f64 x) (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(fma.f64 #s(literal -1 binary64) (*.f64 x y) (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(fma.f64 (neg.f64 x) y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(fma.f64 (*.f64 x #s(literal -1 binary64)) y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x y) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64))) (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 x (.f64 y (*.f64 x y))))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y))))) (fma.f64 (.f64 x y) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 x (.f64 y (*.f64 x y)))) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y)))))) (neg.f64 (fma.f64 (.f64 x y) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 x (.f64 y (*.f64 x y))))) (neg.f64 (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))))
(/.f64 (+.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (.f64 x y)) #s(literal 3 binary64))) (+.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)) (-.f64 (.f64 (neg.f64 (.f64 x y)) (neg.f64 (.f64 x y))) (.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (neg.f64 (.f64 x y))))))
(/.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 (neg.f64 (.f64 x y)) (neg.f64 (.f64 x y)))) (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (neg.f64 (.f64 x y))))
(.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 3 binary64)) (.f64 (.f64 x y) (.f64 x (.f64 y (.f64 x y))))) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x y) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)))))
(.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 2 binary64)) (.f64 x (.f64 y (.f64 x y)))) (/.f64 #s(literal 1 binary64) (fma.f64 x y (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))))
(+.f64 (exp.f64 x) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 x))
(-.f64 (exp.f64 x) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (exp.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x)))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 x)
(/.f64 (expm1.f64 (+.f64 x x)) #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
(/.f64 (expm1.f64 (+.f64 x x)) (-.f64 (exp.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (expm1.f64 (+.f64 x x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))) (expm1.f64 (*.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64))) (+.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))))
(/.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 x) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (*.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (neg.f64 (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x)))))
(*.f64 (expm1.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(.f64 (expm1.f64 (.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x)))))
(.f64 (/.f64 (expm1.f64 (+.f64 x x)) (+.f64 #s(literal 1 binary64) (exp.f64 (.f64 x #s(literal 3 binary64))))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(*.f64 (/.f64 (expm1.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(+.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (exp.f64 (+.f64 x x)))
(-.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64))
(-.f64 (/.f64 (exp.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(-.f64 (/.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(fma.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)) #s(literal -1 binary64))
(fma.f64 (exp.f64 x) (exp.f64 x) #s(literal -1 binary64))
(fma.f64 (exp.f64 (+.f64 x x)) #s(literal 1 binary64) #s(literal -1 binary64))
(expm1.f64 (+.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (expm1.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x)))))
(/.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (-.f64 #s(literal 1 binary64) (.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)))))
(/.f64 (expm1.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))
(/.f64 (expm1.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (-.f64 (exp.f64 (+.f64 x x)) #s(literal -1 binary64)))
(/.f64 (neg.f64 (expm1.f64 (*.f64 (+.f64 x x) #s(literal 3 binary64)))) (neg.f64 (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 (neg.f64 (expm1.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(*.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (expm1.f64 x))
(.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(*.f64 (expm1.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
(+.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(-.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x))) (/.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(fma.f64 #s(literal 1 binary64) (exp.f64 x) #s(literal 1 binary64))
(fma.f64 (exp.f64 x) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (exp.f64 x) (/.f64 (exp.f64 x) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (exp.f64 (+.f64 x x)) (/.f64 #s(literal 1 binary64) (expm1.f64 x)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (+.f64 x x))) #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(fma.f64 (/.f64 (exp.f64 (+.f64 x x)) (expm1.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)) (exp.f64 (+.f64 x x))) (neg.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(neg.f64 (/.f64 (expm1.f64 (+.f64 x x)) (neg.f64 (expm1.f64 x))))
(neg.f64 (/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)) (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (neg.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (expm1.f64 x)))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))
(/.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))) (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x))))
(/.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) (.f64 (expm1.f64 x) (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))) (-.f64 #s(literal 1 binary64) (exp.f64 x)))
(/.f64 (expm1.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (*.f64 (expm1.f64 x) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))))
(/.f64 (-.f64 (.f64 (exp.f64 (+.f64 x x)) (expm1.f64 x)) (.f64 (expm1.f64 x) #s(literal 1 binary64))) (*.f64 (expm1.f64 x) (expm1.f64 x)))
(/.f64 (.f64 (expm1.f64 (.f64 (+.f64 x x) #s(literal 3 binary64))) #s(literal 1 binary64)) (*.f64 (+.f64 (exp.f64 (fma.f64 x #s(literal 2 binary64) (+.f64 x x))) (+.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x)))) (expm1.f64 x)))
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(-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)
(-.f64 (/.f64 (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 y (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 y (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))))))
(-.f64 (/.f64 (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) (/.f64 (.f64 y y) (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))))
(-.f64 (+.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) #s(literal 0 binary64)) y)
(fma.f64 x #s(literal 1/8 binary64) (-.f64 #s(literal 1/2 binary64) y))
(fma.f64 y #s(literal -1 binary64) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y))
(fma.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/16 binary64)))) (neg.f64 y))
(fma.f64 #s(literal -1 binary64) y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))
(fma.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))) (neg.f64 y))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 y (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))))) (-.f64 (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) (.f64 y (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (*.f64 (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y))))
(/.f64 (-.f64 (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) (.f64 y (.f64 y y))) (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (*.f64 y (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))))))
(/.f64 (*.f64 (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)) (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) (.f64 y (.f64 y y)))) (neg.f64 (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (*.f64 y (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (*.f64 (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y))) (neg.f64 (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))))
(/.f64 (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (pow.f64 (neg.f64 y) #s(literal 3 binary64))) (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (-.f64 (.f64 (neg.f64 y) (neg.f64 y)) (*.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (neg.f64 y)))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64) (pow.f64 (-.f64 #s(literal 1/2 binary64) y) #s(literal 3 binary64))) (fma.f64 (.f64 x x) #s(literal 1/64 binary64) (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) y) (-.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 1/2 binary64) y)))))
(/.f64 (-.f64 (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (.f64 (neg.f64 y) (neg.f64 y))) (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (neg.f64 y)))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (.f64 (-.f64 #s(literal 1/2 binary64) y) (-.f64 #s(literal 1/2 binary64) y))) (-.f64 (.f64 x #s(literal 1/8 binary64)) (-.f64 #s(literal 1/2 binary64) y)))
(.f64 (-.f64 (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))) (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) (.f64 y (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))))))
(.f64 (.f64 (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))) (-.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)) y)) (/.f64 #s(literal 1 binary64) (+.f64 y (fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64)))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64)))
(+.f64 (*.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(-.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))))
(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/16 binary64))) (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)) (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1/8 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/16 binary64))))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1/8 binary64)) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64)) (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1/8 binary64))) (neg.f64 (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (.f64 x #s(literal 1/16 binary64)))))
(/.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64))) (neg.f64 (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))))
(/.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal 1/64 binary64))) (-.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64) #s(literal 1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal 1/4 binary64)) (*.f64 x #s(literal 1/16 binary64)))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/64 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/8 binary64) #s(literal -1/2 binary64))))
(log.f64 #s(literal 2 binary64))
(exp.f64 x)
(*.f64 #s(literal 1 binary64) (exp.f64 x))
(*.f64 (exp.f64 x) #s(literal 1 binary64))
(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
(+.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(+.f64 (log.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (log.f64 (expm1.f64 x))))
(-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 x)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(-.f64 (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) (log1p.f64 (.f64 (exp.f64 x) (expm1.f64 x))))
(-.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (log1p.f64 (neg.f64 (exp.f64 x))))
(-.f64 (log.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (log.f64 (neg.f64 (expm1.f64 x))))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (log.f64 (expm1.f64 (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (log.f64 (expm1.f64 x)) #s(literal 3 binary64))) (fma.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 (+.f64 x x))) (fma.f64 (log.f64 (expm1.f64 x)) (log.f64 (expm1.f64 x)) (*.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 x))))))
(/.f64 (-.f64 (.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 (+.f64 x x)))) (.f64 (log.f64 (expm1.f64 x)) (log.f64 (expm1.f64 x)))) (+.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 x))))
(log1p.f64 (exp.f64 x))
(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
(+.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (/.f64 #s(literal 1 binary64) (expm1.f64 x))))
(+.f64 (log.f64 (expm1.f64 (+.f64 x x))) (neg.f64 (log.f64 (expm1.f64 x))))
(-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 x)))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(-.f64 (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) (log1p.f64 (.f64 (exp.f64 x) (expm1.f64 x))))
(-.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (log1p.f64 (neg.f64 (exp.f64 x))))
(-.f64 (log.f64 (neg.f64 (expm1.f64 (+.f64 x x)))) (log.f64 (neg.f64 (expm1.f64 x))))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (log.f64 (expm1.f64 (+.f64 x x))) #s(literal 3 binary64)) (pow.f64 (log.f64 (expm1.f64 x)) #s(literal 3 binary64))) (fma.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 (+.f64 x x))) (fma.f64 (log.f64 (expm1.f64 x)) (log.f64 (expm1.f64 x)) (*.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 x))))))
(/.f64 (-.f64 (.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 (+.f64 x x)))) (.f64 (log.f64 (expm1.f64 x)) (log.f64 (expm1.f64 x)))) (+.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 x))))
(log1p.f64 (exp.f64 x))

eval72.0ms (1%)

Memory: -2.2MiB live, 70.6MiB allocated
Compiler: Compiled 4 594 to 601 computations (86.9% saved)

prune64.0ms (0.9%)

Memory

19.9MiB live, 58.3MiB allocated

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	312	6	318
Fresh	3	0	3
Picked	2	3	5
Done	0	0	0
Total	317	9	326

Accuracy

99.7%

Counts

326 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.5%	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
▶	73.8%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x 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))))
▶	82.5%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
	47.6%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
▶	47.5%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 #s(literal 2 binary64)))
✓	75.4%	#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))))
▶	98.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
✓	53.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
✓	48.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))

Compiler

Compiled 141 to 103 computations (27% saved)

simplify479.0ms (6.5%)

Memory

-33.4MiB live, 462.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal 1/8 binary64))
✓	cost-diff	0	(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))
✓	cost-diff	0	(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)))
✓	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	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
✓	cost-diff	0	(neg.f64 y)
✓	cost-diff	512	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
✓	cost-diff	0	(log.f64 #s(literal 2 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	1216	(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
✓	cost-diff	6400	(log1p.f64 (exp.f64 x))

Rules

11 990×	`lower-fma.f32`
11 980×	`lower-fma.f64`
2 404×	`lower-*.f32`
2 400×	`lower-*.f64`
2 366×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	167
0	61	138
1	113	138
2	202	138
3	398	138
4	805	138
5	1584	138
6	3059	138
7	4870	138
8	7706	138
0	8154	138

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.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 (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 #s(literal 2 binary64)))
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
(neg.f64 y)
y
x
(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
#s(literal 2 binary64)
#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (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)
#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x 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))))
(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)))
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))
(fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal 1/8 binary64))
#s(literal -1/192 binary64)
(*.f64 x x)
#s(literal 1/8 binary64)
(-.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(log.f64 #s(literal 2 binary64))
#s(literal 2 binary64)

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

localize122.0ms (1.7%)

Memory

17.7MiB live, 259.0MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(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)))
✓	accuracy	100.0%	(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))
✓	accuracy	99.9%	(fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal 1/8 binary64))
✓	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	100.0%	(neg.f64 y)
✓	accuracy	100.0%	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
✓	accuracy	97.7%	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
✓	accuracy	100.0%	(log.f64 #s(literal 2 binary64))
✓	accuracy	100.0%	(-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)
✓	accuracy	99.8%	(*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y))
✓	accuracy	99.8%	(/.f64 (log1p.f64 (exp.f64 x)) x)
✓	accuracy	98.1%	(log1p.f64 (exp.f64 x))

Samples

70.0ms	237×	0	valid
14.0ms	19×	1	valid

Compiler

Compiled 191 to 37 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 65.0ms

ival-mult: 19.0ms (29.4% of total)

ival-log: 10.0ms (15.5% of total)

ival-add: 8.0ms (12.4% of total)

ival-exp: 5.0ms (7.7% of total)

ival-sub: 5.0ms (7.7% of total)

ival-div: 4.0ms (6.2% of total)

const: 4.0ms (6.2% of total)

ival-expm1: 3.0ms (4.6% of total)

ival-log1p: 3.0ms (4.6% of total)

ival-neg: 2.0ms (3.1% of total)

adjust: 1.0ms (1.5% of total)

exact: 1.0ms (1.5% of total)

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

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

series29.0ms (0.4%)

Memory

-24.9MiB live, 52.9MiB allocated

Counts

14 → 228

Calls

Call 1

Inputs
#<alt (log1p.f64 (exp.f64 x))>
#<alt (*.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 (log.f64 #s(literal 2 binary64))>
#<alt (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))>
#<alt (neg.f64 y)>
#<alt (log.f64 #s(approx (+ 1 (exp x)) #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 (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)))>
#<alt (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))>
#<alt (fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal 1/8 binary64))>
#<alt (*.f64 x 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 (+ (* -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) 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 (+ 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 (* -1 y))))>
#<alt (+ (log 2) (* x (+ 1/2 (+ (* -1 y) (* 1/8 x)))))>
#<alt (+ (log 2) (* x (+ 1/2 (+ (* -1 y) (* x (+ 1/8 (* -1/192 (pow x 2))))))))>
#<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 (* -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) (* 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 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 (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 (* -1/192 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* (pow x 4) (- (+ (/ 1/2 (pow x 3)) (* 1/8 (/ 1 (pow x 2)))) (+ 1/192 (/ y (pow x 3)))))>
#<alt (* (pow x 4) (- (+ (/ 1/2 (pow x 3)) (+ (* 1/8 (/ 1 (pow x 2))) (/ (log 2) (pow x 4)))) (+ 1/192 (/ y (pow x 3)))))>
#<alt (* -1/192 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* (pow x 4) (- (+ (/ 1/2 (pow x 3)) (* 1/8 (/ 1 (pow x 2)))) (+ 1/192 (/ y (pow x 3)))))>
#<alt (* (pow x 4) (- (+ (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) (pow x 3))) (* 1/8 (/ 1 (pow x 2)))) 1/192))>
#<alt (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))))>
#<alt (+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))))>
#<alt (* -1 (* x y))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) y))))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) y))))>
#<alt (* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))) y))))>
#<alt (* -1 (* x y))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) y)))))>
#<alt (* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) y)))))>
#<alt (- 1/2 y)>
#<alt (- (+ 1/2 (* 1/8 x)) y)>
#<alt (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)>
#<alt (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)>
#<alt (* -1/192 (pow x 3))>
#<alt (* (pow x 3) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (* 1/8 (/ 1 (pow x 2)))) (+ 1/192 (/ y (pow x 3)))))>
#<alt (* (pow x 3) (- (+ (/ 1/2 (pow x 3)) (* 1/8 (/ 1 (pow x 2)))) (+ 1/192 (/ y (pow x 3)))))>
#<alt (* -1/192 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- 1/192 (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- (+ 1/192 (* -1 (/ (- 1/2 y) (pow x 3)))) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (* -1 (* (pow x 3) (- (+ 1/192 (* -1 (/ (- 1/2 y) (pow x 3)))) (* 1/8 (/ 1 (pow x 2))))))>
#<alt (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2)))))>
#<alt (+ 1/2 (+ (* -1 y) (* x (+ 1/8 (* -1/192 (pow x 2))))))>
#<alt (+ 1/2 (+ (* -1 y) (* x (+ 1/8 (* -1/192 (pow x 2))))))>
#<alt (+ 1/2 (+ (* -1 y) (* x (+ 1/8 (* -1/192 (pow x 2))))))>
#<alt (* -1 y)>
#<alt (* y (- (+ (* 1/2 (/ 1 y)) (/ (* x (+ 1/8 (* -1/192 (pow x 2)))) y)) 1))>
#<alt (* y (- (+ (* 1/2 (/ 1 y)) (/ (* x (+ 1/8 (* -1/192 (pow x 2)))) y)) 1))>
#<alt (* y (- (+ (* 1/2 (/ 1 y)) (/ (* x (+ 1/8 (* -1/192 (pow x 2)))) y)) 1))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))))>
#<alt (* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))))>
#<alt 1/8>
#<alt (+ 1/8 (* -1/192 (pow x 2)))>
#<alt (+ 1/8 (* -1/192 (pow x 2)))>
#<alt (+ 1/8 (* -1/192 (pow x 2)))>
#<alt (* -1/192 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* -1/192 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192))>
#<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)>

Calls

57 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	(/ (log (+ 1 (exp x))) x)
5.0ms	x	@	-inf	(/ (log (+ 1 (exp x))) x)
3.0ms	x	@	-inf	(* x (- (/ (log (+ 1 (exp x))) x) y))
3.0ms	y	@	0	(+ (* x (+ (* x (+ (* -1/192 (* x x)) 1/8)) (- 1/2 y))) (log 2))
1.0ms	x	@	0	(+ (* x (- 1/2 y)) (log 2))

simplify326.0ms (4.4%)

Memory

7.9MiB live, 459.0MiB allocated

Algorithm

1×	egg-herbie

Rules

11 270×	`lower-fma.f64`
11 270×	`lower-fma.f32`
3 246×	`lower-+.f64`
3 246×	`lower-+.f32`
3 146×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	166	1957
1	492	1949
2	1419	1920
3	4420	1830
0	8456	1550

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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

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

rewrite426.0ms (5.8%)

Memory

0.2MiB live, 712.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 288×	`lower-fma.f32`
5 278×	`lower-fma.f64`
4 194×	`lower-/.f32`
4 192×	`lower-/.f64`
4 110×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	83
0	48	83
1	188	83
2	1459	83
0	8337	83

Stop Event

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

Counts

14 → 545

Calls

Call 1

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

Outputs
(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
(+.f64 (log1p.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))))
(+.f64 (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) (neg.f64 (log1p.f64 (.f64 (exp.f64 x) (expm1.f64 x)))))
(+.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(+.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (neg.f64 (log1p.f64 (neg.f64 (exp.f64 x)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(-.f64 (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) (log1p.f64 (.f64 (exp.f64 x) (expm1.f64 x))))
(-.f64 (log1p.f64 (exp.f64 (*.f64 x #s(literal 3 binary64)))) (log.f64 (+.f64 (exp.f64 (+.f64 x x)) (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (log1p.f64 (neg.f64 (exp.f64 x))))
(-.f64 (log.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (exp.f64 (*.f64 x #s(literal 3 binary64)))))) (log.f64 (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) #s(literal 1 binary64)))))
(-.f64 (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 (+.f64 x x))))) (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (exp.f64 x)))))
(-.f64 (log.f64 (expm1.f64 (+.f64 x x))) (log.f64 (expm1.f64 x)))
(neg.f64 (neg.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) #s(literal 3 binary64)) (pow.f64 (log1p.f64 (.f64 (exp.f64 x) (expm1.f64 x))) #s(literal 3 binary64))) (fma.f64 (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) (fma.f64 (log1p.f64 (.f64 (exp.f64 x) (expm1.f64 x))) (log1p.f64 (.f64 (exp.f64 x) (expm1.f64 x))) (.f64 (log1p.f64 (exp.f64 (.f64 x #s(literal 3 binary64)))) (log1p.f64 (*.f64 (exp.f64 x) (expm1.f64 x)))))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) #s(literal 3 binary64)) (pow.f64 (log1p.f64 (neg.f64 (exp.f64 x))) #s(literal 3 binary64))) (fma.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (fma.f64 (log1p.f64 (neg.f64 (exp.f64 x))) (log1p.f64 (neg.f64 (exp.f64 x))) (*.f64 (log1p.f64 (neg.f64 (exp.f64 (+.f64 x x)))) (log1p.f64 (neg.f64 (exp.f64 x)))))))
(log1p.f64 (exp.f64 x))
(+.f64 (.f64 x (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x)) (.f64 x (neg.f64 y)))
(+.f64 (.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) x) (.f64 x (neg.f64 y)))
(fma.f64 x (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (*.f64 x (neg.f64 y)))
(fma.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) x (*.f64 x (neg.f64 y)))
(/.f64 x (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64))) (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64))) (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y)) x)))
(/.f64 (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y)))) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y))) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y))
(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y))) x) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y)) x) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y))
(/.f64 (neg.f64 (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y))))) (neg.f64 (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y)))) (neg.f64 (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (*.f64 y y))) x)) (neg.f64 (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (.f64 y y)) x)) (neg.f64 (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)))
(/.f64 (+.f64 (pow.f64 (.f64 x (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x)) #s(literal 3 binary64)) (.f64 (.f64 x (neg.f64 y)) (.f64 (.f64 x x) (.f64 y y)))) (fma.f64 (.f64 x (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x)) (.f64 x (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x)) (-.f64 (.f64 (.f64 x x) (.f64 y y)) (.f64 (.f64 x (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x)) (.f64 x (neg.f64 y))))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) x) #s(literal 3 binary64)) (.f64 (.f64 x (neg.f64 y)) (.f64 (.f64 x x) (.f64 y y)))) (fma.f64 (.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) x) (.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) x) (-.f64 (.f64 (.f64 x x) (.f64 y y)) (.f64 (.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) x) (.f64 x (neg.f64 y))))))
(*.f64 x (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y))
(*.f64 (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) x)
(.f64 (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(.f64 (.f64 x (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)))
(.f64 (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y))) x) (/.f64 #s(literal 1 binary64) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(.f64 (.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y)) x) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)))
(+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y))
(+.f64 (neg.f64 y) (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x))
(+.f64 (/.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)) (neg.f64 (/.f64 (*.f64 y y) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y))))
(+.f64 (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 0 binary64)) (neg.f64 y))
(-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)
(-.f64 (/.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))) (/.f64 (.f64 y (.f64 y y)) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))))
(-.f64 (/.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)) (/.f64 (*.f64 y y) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)))
(-.f64 (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 0 binary64)) y)
(-.f64 (/.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y))) (/.f64 (*.f64 y y) (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y))))
(fma.f64 y #s(literal -1 binary64) (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x))
(fma.f64 #s(literal 1 binary64) (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y))
(fma.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) x) (neg.f64 y))
(fma.f64 (neg.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 x)) (neg.f64 y))
(fma.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (.f64 y (.f64 y y)) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)) (neg.f64 (/.f64 (*.f64 y y) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (neg.f64 y))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (neg.f64 y))
(fma.f64 #s(literal -1 binary64) y (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x))
(fma.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))) (neg.f64 y))
(fma.f64 (*.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x) (neg.f64 y))
(fma.f64 (-.f64 #s(literal 0 binary64) (.f64 y (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (fma.f64 y y (*.f64 #s(literal 0 binary64) y)))) (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x))
(fma.f64 (-.f64 #s(literal 0 binary64) (*.f64 y y)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) y)) (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (-.f64 (.f64 y y) (.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y)))) (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y)) (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y))))
(/.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y))) (fma.f64 y (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y) (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 3 binary64)) (.f64 y (.f64 y y))) (+.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (-.f64 (.f64 y y) (.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y))))
(/.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y)) (+.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) y))
(/.f64 (-.f64 (pow.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) #s(literal 2 binary64)) (*.f64 y y)) (-.f64 (/.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) x) (neg.f64 y)))
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(.f64 (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/2 binary64) y) (-.f64 #s(literal 1/2 binary64) y)) (.f64 (.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64))) (.f64 x (.f64 (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)))))))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 #s(literal 1/2 binary64) y) (-.f64 (-.f64 #s(literal 1/2 binary64) y) (.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)))) (.f64 x (.f64 (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) (.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)))))))))
(.f64 (neg.f64 (.f64 (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)) (+.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))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.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))))
(.f64 (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (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 (.f64 y (.f64 y y)))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (fma.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (fma.f64 y y (.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)))))
(.f64 (-.f64 (.f64 (-.f64 #s(literal 1/2 binary64) y) (-.f64 #s(literal 1/2 binary64) y)) (.f64 x (.f64 (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) (.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)))))) (/.f64 #s(literal 1 binary64) (-.f64 (-.f64 #s(literal 1/2 binary64) y) (.f64 x (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64))))))
(.f64 (fma.f64 (fma.f64 x (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)) #s(literal 1/2 binary64)) (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 (.f64 y y))) (/.f64 #s(literal 1 binary64) (+.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)))
(+.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/192 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal -1/192 binary64) (.f64 x x)) #s(literal 1/8 binary64))
(+.f64 (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (neg.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64)))))
(-.f64 (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))))
(-.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/192 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/192 binary64) (.f64 x x)))))
(fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64))
(fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal 1/8 binary64))
(fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64))
(fma.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (neg.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64)))))
(fma.f64 (*.f64 x #s(literal -1/192 binary64)) x #s(literal 1/8 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/64 binary64) (-.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) #s(literal -1/1536 binary64)))) (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (*.f64 x x)) #s(literal 1/512 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/192 binary64) (.f64 x x))) (-.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) (-.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 x x) #s(literal -1/1536 binary64))))
(/.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) (+.f64 #s(literal 1/64 binary64) (-.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/1536 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)))))
(/.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64)) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64)))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64))) (neg.f64 (-.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 x x) #s(literal -1/1536 binary64)))))
(/.f64 (neg.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (-.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (*.f64 x x) #s(literal -1/1536 binary64))))))
(/.f64 (neg.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64))) (neg.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (-.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)))) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/192 binary64) (.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64)) #s(literal 1/64 binary64))) (.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64)) (fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal -1/8 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64)))) (neg.f64 (neg.f64 (-.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (.f64 x x) #s(literal -1/1536 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64)))) (neg.f64 (neg.f64 (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/192 binary64) (.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (fma.f64 (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (.f64 (/.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (fma.f64 #s(literal -1/192 binary64) (.f64 x x) #s(literal -1/8 binary64))) (/.f64 #s(literal 1/64 binary64) (fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal -1/8 binary64)))))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x #s(literal -1/192 binary64)) #s(literal 1/8 binary64)))
(.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (*.f64 x x) #s(literal -1/1536 binary64)))))
(.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (-.f64 (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x))) (.f64 (.f64 x x) #s(literal -1/1536 binary64))))))
(.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal -1/8 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 #s(literal -1/7077888 binary64) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)) #s(literal 1/512 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/64 binary64)) (.f64 (*.f64 x x) #s(literal -1/1536 binary64))))))
(.f64 (neg.f64 (fma.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)) #s(literal -1/64 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal -1/192 binary64) (*.f64 x x) #s(literal -1/8 binary64)))))
(.f64 (-.f64 #s(literal 1/64 binary64) (.f64 #s(literal 1/36864 binary64) (.f64 (.f64 x x) (.f64 x x)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (.f64 #s(literal -1/192 binary64) (*.f64 x x)))))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

eval15.0ms (0.2%)

Memory: 5.6MiB live, 42.7MiB allocated
Compiler: Compiled 1 841 to 258 computations (86% saved)

prune14.0ms (0.2%)

Memory

9.0MiB live, 47.0MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	5	5
Done	0	3	3
Total	118	9	127

Accuracy

99.7%

Counts

127 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	91.5%	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
✓	73.8%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x 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))))
✓	82.5%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
▶	47.6%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
✓	47.5%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 #s(literal 2 binary64)))
✓	75.4%	#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))))
✓	98.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
✓	53.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
✓	48.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))

Compiler

Compiled 82 to 60 computations (26.8% saved)

simplify366.0ms (5%)

Memory

-15.4MiB live, 581.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x x)
✓	cost-diff	0	(expm1.f64 (+.f64 x x))
✓	cost-diff	192	(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
✓	cost-diff	7104	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))

Rules

13 358×	`lower-fma.f64`
13 358×	`lower-fma.f32`
2 664×	`lower--.f64`
2 664×	`lower--.f32`
2 210×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	37
0	24	37
1	42	37
2	63	37
3	95	34
4	153	28
5	240	28
6	585	28
7	2410	28
8	7745	28
0	8061	24

Stop Event

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

Calls

Call 1

Inputs
#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
x
(expm1.f64 x)

Outputs
#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log1p.f64 (exp.f64 x)))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(log1p.f64 (exp.f64 x))
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
x
(expm1.f64 x)

localize83.0ms (1.1%)

Memory

8.9MiB live, 162.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(expm1.f64 (+.f64 x x))
✓	accuracy	100.0%	(expm1.f64 x)
✓	accuracy	98.0%	(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
✓	accuracy	97.7%	(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))

Samples

49.0ms	66×	2	valid
16.0ms	172×	0	valid
7.0ms	18×	1	valid

Compiler

Compiled 55 to 11 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-log: 39.0ms (63.4% of total)

ival-expm1: 7.0ms (11.4% of total)

ival-mult: 6.0ms (9.8% of total)

ival-div: 3.0ms (4.9% of total)

adjust: 3.0ms (4.9% of total)

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

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

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

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

series1.0ms (0%)

Memory

3.9MiB live, 3.9MiB allocated

Counts

5 → 60

Calls

Call 1

Inputs
#<alt (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))>
#<alt (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))>
#<alt (expm1.f64 (+.f64 x x))>
#<alt (+.f64 x x)>
#<alt (expm1.f64 x)>

Outputs
#<alt 2>
#<alt (+ 2 x)>
#<alt (+ 2 (* x (+ 1 (* 1/2 x))))>
#<alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1))>
#<alt (/ (- (exp (neg (* -2 x))) 1) (- (exp 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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 2 x)))>
#<alt (* x (+ 2 (* x (+ 2 (* 4/3 x)))))>
#<alt (* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (* 2 x)) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (- (exp (neg (* -2 x))) 1)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 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)>

Calls

15 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	(+ x x)
0.0ms	x	@	0	(+ x x)
0.0ms	x	@	-inf	(- (exp (+ x x)) 1)
0.0ms	x	@	0	(/ (- (exp (+ x x)) 1) (- (exp x) 1))
0.0ms	x	@	-inf	(+ x x)

simplify407.0ms (5.5%)

Memory

7.1MiB live, 603.3MiB allocated

Algorithm

1×	egg-herbie

Rules

14 856×	`lower-fma.f64`
14 856×	`lower-fma.f32`
3 504×	`lower-*.f64`
3 504×	`lower-*.f32`
2 380×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	430
1	210	430
2	474	430
3	1196	430
4	2382	350
5	3701	318
6	6521	318
0	8332	247

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 59

Calls

Call 1

Inputs
2
(+ 2 x)
(+ 2 (* x (+ 1 (* 1/2 x))))
(+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x))))))
(/ (- (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) (- (exp 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 (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (* 2 x)) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(log (/ (- (exp (neg (* -2 x))) 1) (- (exp x) 1)))
(* 2 x)
(* x (+ 2 (* 2 x)))
(* x (+ 2 (* x (+ 2 (* 4/3 x)))))
(* x (+ 2 (* x (+ 2 (* x (+ 4/3 (* 2/3 x)))))))
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (* 2 x)) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(- (exp (neg (* -2 x))) 1)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 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)

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

rewrite64.0ms (0.9%)

Memory

7.5MiB live, 85.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

224×	`lower-/.f32`
222×	`lower-/.f64`
194×	`lower-fma.f64`
194×	`lower-fma.f32`
186×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	24
0	14	24
1	64	18
0	482	16

Stop Event

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

Counts

5 → 100

Calls

Call 1

Inputs
(/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))
(log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x)))
(expm1.f64 (+.f64 x x))
(+.f64 x x)
(expm1.f64 x)

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune6.0ms (0.1%)

Memory

12.9MiB live, 12.9MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	8	8
Total	9	9

Accuracy

99.7%

Counts

9 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	91.5%	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
✓	73.8%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x 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))))
✓	82.5%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (fma.f64 x (-.f64 #s(literal 1/2 binary64) y) (log.f64 #s(literal 2 binary64))))
✓	47.6%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 (/.f64 (expm1.f64 (+.f64 x x)) (expm1.f64 x))))
✓	47.5%	#s(approx (- (log (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (log.f64 #s(literal 2 binary64)))
✓	75.4%	#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))))
✓	98.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (-.f64 (/.f64 (log1p.f64 (exp.f64 x)) x) y)))
✓	53.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y)))
✓	48.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))

Compiler

Compiled 199 to 96 computations (51.8% saved)

regimes16.0ms (0.2%)

Memory

-9.5MiB live, 29.6MiB allocated

Counts

15 → 2

Calls

Call 1

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

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

Calls

3 calls:

5.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
5.0ms	x
5.0ms	y

Results

Accuracy	Segments	Branch
99.7%	2	`x`
98.1%	1	`y`
99.7%	2	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes39.0ms (0.5%)

Memory

-10.6MiB live, 50.0MiB allocated

Counts

11 → 2

Calls

Call 1

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

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:

31.0ms	x
4.0ms	y
4.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
91.5%	1	`y`
99.1%	2	`x`
98.4%	2	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

regimes4.0ms (0.1%)

Memory

-31.6MiB live, 7.6MiB allocated

Counts

7 → 2

Calls

Call 1

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

4.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes3.0ms (0%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

5 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
98.9%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes2.0ms (0%)

Memory

5.3MiB live, 5.3MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#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 (/ (- (exp (+ x x)) 1) (- (exp x) 1))) (* x y)) (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:

2.0ms

Results

Accuracy	Segments	Branch
98.8%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes4.0ms (0.1%)

Memory

8.7MiB live, 8.7MiB allocated

Counts

3 → 3

Calls

Call 1

Inputs

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

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

Calls

2 calls:

2.0ms	x
2.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
97.4%	3	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
82.9%	3	`x`

Compiler

Compiled 14 to 10 computations (28.6% saved)

regimes4.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
53.3%	1	`x`
53.3%	1	`y`
53.3%	1	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 17 to 12 computations (29.4% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.0418980501966437e+281	3.52539135245147e+281

Compiler

Compiled 14 to 13 computations (7.1% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-244.79795389636345	-1.0250790967379647e-5

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-244.79795389636345	-1.0250790967379647e-5

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-244.79795389636345	-1.0250790967379647e-5

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-244.79795389636345	-1.0250790967379647e-5

Compiler

Compiled 14 to 11 computations (21.4% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	438.7693264127335	5532.5395615853995
0.0ms	4.233052376933856e-34	0.6930889346142685

Compiler

Compiled 14 to 13 computations (7.1% saved)

simplify9.0ms (0.1%)

Memory

-22.0MiB live, 17.4MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	247
1	66	247
2	77	247
3	82	247
4	84	247

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 300000000000000009834673794858629474571211584906448069279000073232282780959212300778380313601723537916145249274547245245610490403073208708798197330387912756337433641273686019744581981706544878947098564673753090188727780417733450695639284569447801386623635703043256531710379410063360 binary64)) (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.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 -200 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 -200 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 -200 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y))) (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -200 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 1461501637330903/2923003274661805836407369665432566039311865085952 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 500 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)))

Outputs
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 300000000000000009834673794858629474571211584906448069279000073232282780959212300778380313601723537916145249274547245245610490403073208708798197330387912756337433641273686019744581981706544878947098564673753090188727780417733450695639284569447801386623635703043256531710379410063360 binary64)) (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.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 -200 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 -200 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 -200 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 -200 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 -200 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 x (neg.f64 y))) (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -200 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (neg.f64 (*.f64 x y))) (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -200 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 -200 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 1461501637330903/2923003274661805836407369665432566039311865085952 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 500 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 1461501637330903/2923003274661805836407369665432566039311865085952 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 500 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)))

soundness865.0ms (11.8%)

Memory

19.2MiB live, 367.4MiB allocated

Rules

11 474×	`lower-fma.f64`
11 474×	`lower-fma.f32`
4 436×	`lower-/.f64`
4 436×	`lower-/.f32`
3 924×	`lower-*.f32`

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
0	67	400
1	180	400
2	389	400
3	1353	400
4	4014	370
5	6856	370
0	8132	300
0	26	79
0	47	79
1	182	66
0	1414	66

Stop Event

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

Compiler

Compiled 223 to 104 computations (53.4% saved)

preprocess99.0ms (1.3%)

Memory: 1.9MiB live, 81.6MiB allocated
Compiler: Compiled 336 to 124 computations (63.1% 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 (1%)

sample1.4s (19.1%)

preprocess34.0ms (0.5%)

explain145.0ms (2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.2%)

localize37.0ms (0.5%)

series65.0ms (0.9%)

simplify287.0ms (3.9%)

rewrite372.0ms (5.1%)

eval53.0ms (0.7%)

prune54.0ms (0.7%)

simplify483.0ms (6.6%)

localize143.0ms (1.9%)

series98.0ms (1.3%)

simplify439.0ms (6%)

rewrite128.0ms (1.7%)

eval72.0ms (1%)

prune64.0ms (0.9%)

simplify479.0ms (6.5%)

localize122.0ms (1.7%)

series29.0ms (0.4%)

simplify326.0ms (4.4%)

rewrite426.0ms (5.8%)

eval15.0ms (0.2%)

prune14.0ms (0.2%)

simplify366.0ms (5%)

localize83.0ms (1.1%)

series1.0ms (0%)

simplify407.0ms (5.5%)

rewrite64.0ms (0.9%)

eval0.0ms (0%)

prune6.0ms (0.1%)

regimes16.0ms (0.2%)

regimes39.0ms (0.5%)

regimes4.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

regimes4.0ms (0.1%)

regimes4.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify9.0ms (0.1%)

soundness865.0ms (11.8%)

preprocess99.0ms (1.3%)

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