Metrics for Logistic regression 2

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze66.0ms (1%)

Memory

-18.5MiB live, 140.6MiB 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)

sample1.1s (16.8%)

Memory

43.4MiB live, 1 835.6MiB allocated

Samples

508.0ms	8 256×	0	valid
234.0ms	2 694×	1	exit

Precisions

Click to see histograms. Total time spent on operations: 417.0ms

ival-log1p: 132.0ms (31.6% of total)

ival-exp: 95.0ms (22.8% of total)

ival-mult: 84.0ms (20.1% of total)

ival-sub: 53.0ms (12.7% of total)

adjust: 41.0ms (9.8% of total)

ival-true: 9.0ms (2.2% of total)

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

Bogosity

explain94.0ms (1.4%)

Memory

17.9MiB live, 178.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
1	75	(-1.3542865956477827e+29 -4.079680377525516e-218)	-	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`
0	0	-	-	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
0	0	-	-	`(+.f64 #s(literal 1 binary64) (exp.f64 x))`
0	0	-	-	`y`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`(*.f64 x y)`
0	0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`	sensitivity	75	0
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`	oflow-rescue	1	0
↳	`(exp.f64 x)`	overflow	1
↳	`(+.f64 #s(literal 1 binary64) (exp.f64 x))`	overflow	1

Confusion

	Predicted +	Predicted -
+	1	0
-	75	180

Precision

0.013157894736842105

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	75	0	180

Precision?

0.013157894736842105

Recall?

1.0

Freqs

test

number	freq
0	180
1	76

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms

512×

valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

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

ival-log1p: 6.0ms (31.2% of total)

ival-exp: 4.0ms (20.8% of total)

ival-mult: 4.0ms (20.8% of total)

ival-sub: 2.0ms (10.4% of total)

ival-add: 2.0ms (10.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess39.0ms (0.6%)

Memory

-41.0MiB live, 36.1MiB 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))
(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))

Compiler

Compiled 9 to 8 computations (11.1% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify10.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
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))
(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))
(log1p.f64 (exp.f64 x))
(+.f64 #s(literal 1 binary64) (exp.f64 x))
(+.f64 (exp.f64 x) #s(literal 1 binary64))
#s(literal 1 binary64)
(exp.f64 x)
x
(*.f64 x y)
(*.f64 y x)
y

localize116.0ms (1.7%)

Memory

-8.4MiB live, 30.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(exp.f64 x)
accuracy	0.0078125	(+.f64 #s(literal 1 binary64) (exp.f64 x))
accuracy	0.015625	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
accuracy	0.24598030713999228	(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Samples

110.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-log1p: 5.0ms (44.2% of total)

ival-exp: 2.0ms (17.7% of total)

ival-mult: 2.0ms (17.7% of total)

ival-sub: 1.0ms (8.8% of total)

ival-add: 1.0ms (8.8% of total)

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

exact: 0.0ms (0% of total)

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

series58.0ms (0.9%)

Memory

2.0MiB live, 78.3MiB allocated

Counts

4 → 60

Calls

Call 1

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

Outputs
#s(alt (log (+ 1 (exp x))) (taylor 0 y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (log (+ 1 (exp x))) y) x)) (taylor inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (log (+ 1 (exp x))) y) x)) (taylor inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* y (- (/ (log (+ 1 (exp x))) y) x)) (taylor inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor -inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x)))) (taylor -inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x)))) (taylor -inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x)))) (taylor -inf y) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (log 2) (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* 1/2 x)) (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* x (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))))) (taylor 0 x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (log 2) (taylor 0 x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* x (- 1/2 y))) (taylor 0 x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y))) (taylor 0 x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y))) (taylor 0 x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt 2 (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 2 x) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 2 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* 1/2 x)))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (+ 1 (* x (+ 1 (* x (+ 1/2 (* 1/6 x)))))) (taylor 0 x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ (log (+ 1 (exp x))) x) y)) (taylor inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ (log (+ 1 (exp x))) x) y)) (taylor inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ (log (+ 1 (exp x))) x) y)) (taylor inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (patch (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor -inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) (patch (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (+ 1 (exp x)) (taylor -inf x) (#s(alt (+.f64 #s(literal 1 binary64) (exp.f64 x)) (patch (+.f64 #s(literal 1 binary64) (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())
#s(alt (exp x) (taylor -inf x) (#s(alt (exp.f64 x) (patch (exp.f64 x) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
26.0ms	x	@	inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x))
20.0ms	x	@	-inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x))
6.0ms	y	@	0	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x))
3.0ms	y	@	-inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x))
1.0ms	y	@	inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x))

simplify121.0ms (1.8%)

Memory

-9.4MiB live, 105.8MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	385
1	180	370
2	389	370
3	1351	370
4	4010	370
5	6711	370
0	8052	300

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

rewrite159.0ms (2.4%)

Memory

32.3MiB live, 186.5MiB allocated

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
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eval64.0ms (1%)

Memory: -27.3MiB live, 92.7MiB allocated
Compiler: Compiled 13 451 to 1 462 computations (89.1% saved)

prune13.0ms (0.2%)

Memory

-6.2MiB live, 33.2MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

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

Accuracy

99.7%

Counts

420 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.9%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
	78.0%	(.f64 (pow.f64 (fma.f64 y x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) #s(literal 2 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal -1 binary64)))
▶	73.6%	(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
▶	75.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))))
	81.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))))
▶	86.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64))))
▶	48.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
	52.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))
	51.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))

Compiler

Compiled 182 to 158 computations (13.2% saved)

simplify295.0ms (4.4%)

Memory

23.1MiB live, 145.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))
cost-diff	448	(*.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))
cost-diff	6336	(log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)))
cost-diff	12800	(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64))
cost-diff	0	(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (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 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64))))
cost-diff	0	(neg.f64 y)
cost-diff	0	(*.f64 (neg.f64 y) x)
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
cost-diff	0	(*.f64 x y)
cost-diff	0	#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
cost-diff	0	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
cost-diff	0	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))

Rules

8 548×	`lower-fma.f32`
8 538×	`lower-fma.f64`
1 436×	`lower-*.f32`
1 428×	`lower-*.f64`
1 412×	`lower-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	211
0	59	213
1	97	210
2	143	200
3	335	200
4	768	200
5	1473	200
6	2671	200
7	4183	200
8	5007	200
9	5223	200
10	5287	200
11	5412	200
12	5452	200
13	5474	200
14	5478	200
15	5478	200
16	5480	200
17	5820	200
18	5820	200
19	5820	200
0	5820	200

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize141.0ms (2.1%)

Memory

-21.9MiB live, 134.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.08328878162065376	(pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))
accuracy	0.24207405713999228	(log1p.f64 (exp.f64 x))
accuracy	0.9170801532532297	(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)))
accuracy	3.8114345758108947	(log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)))
accuracy	0.0078125	(fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y))
accuracy	0.01953125	(fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))
accuracy	0.0234375	(fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64))
accuracy	9.01917953238589	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))))
accuracy	0	(-.f64 #s(literal 1/2 binary64) y)
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	0.01171875	(fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64)))
accuracy	4.021356094413845	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64))))
accuracy	0	(*.f64 (neg.f64 y) x)
accuracy	0	(neg.f64 y)
accuracy	32.922419163937256	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
accuracy	0	(*.f64 x y)
accuracy	0.01171875	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
accuracy	0.24598030713999228	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
accuracy	8.619171513625004	#s(approx (+ 1 (exp x)) #s(literal 2 binary64))

Samples

59.0ms	193×	0	valid
16.0ms	63×	0	invalid

Compiler

Compiled 208 to 33 computations (84.1% saved)

Precisions

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

ival-mult: 12.0ms (26.8% of total)

ival-add: 7.0ms (15.7% of total)

ival-exp: 6.0ms (13.4% of total)

ival-log: 6.0ms (13.4% of total)

const: 4.0ms (8.9% of total)

ival-log1p: 3.0ms (6.7% of total)

ival-pow: 3.0ms (6.7% of total)

ival-sub: 2.0ms (4.5% of total)

exact: 1.0ms (2.2% of total)

ival-neg: 1.0ms (2.2% of total)

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

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

series64.0ms (1%)

Memory

32.0MiB live, 105.4MiB allocated

Counts

20 → 384

Calls

Call 1

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

Outputs
#s(alt (log (+ 1 (exp x))) (taylor 0 y) (#s(alt (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) (patch (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) (patch (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) (patch (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) (patch (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (* x y) (taylor 0 y) (#s(alt (.f64 x y) (patch (.f64 x y) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) (*.f64 (neg.f64 y) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) (*.f64 (neg.f64 y) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) (*.f64 (neg.f64 y) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) (*.f64 (neg.f64 y) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor 0 y) (#s(alt (.f64 (neg.f64 y) x) (patch (.f64 (neg.f64 y) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor 0 y) (#s(alt (.f64 (neg.f64 y) x) (patch (.f64 (neg.f64 y) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor 0 y) (#s(alt (.f64 (neg.f64 y) x) (patch (.f64 (neg.f64 y) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor 0 y) (#s(alt (.f64 (neg.f64 y) x) (patch (.f64 (neg.f64 y) x) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 4) (- (+ (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) (pow x 3))) (* 1/8 (/ 1 (pow x 2)))) 1/192)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))) (patch (fma.f64 (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1/192 (pow x 3)) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- 1/192 (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (+ 1/192 (* -1 (/ (- 1/2 y) (pow x 3)))) (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (+ 1/192 (* -1 (/ (- 1/2 y) (pow x 3)))) (* 1/8 (/ 1 (pow x 2)))))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) (patch (fma.f64 (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) #<representation binary64>) () ())) ())
#s(alt (* -1/192 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- (* 1/8 (/ 1 (pow x 2))) 1/192)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) (patch (fma.f64 (.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x))))) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x))))) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ y (* -1 (/ (log (+ 1 (exp x))) x))))) (taylor -inf x) (#s(alt (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log (/ -1 x)) (log (/ 1 y))) (taylor -inf x) (#s(alt (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) (patch (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log (/ -1 x)) (+ (log (/ 1 y)) (/ (log (+ 1 (exp x))) (* x y)))) (taylor -inf x) (#s(alt (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) (patch (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log (/ -1 x)) (+ (log (/ 1 y)) (* -1 (/ (+ (* -1 (/ (log (+ 1 (exp x))) y)) (* -1/2 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2))) (* 2 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2)))) x))) x)))) (taylor -inf x) (#s(alt (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) (patch (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (log (/ -1 x)) (+ (log (/ 1 y)) (* -1 (/ (+ (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 (/ (+ (* -1/6 (/ (+ (* -6 (/ (pow (log (+ 1 (exp x))) 3) (pow y 3))) (+ (* -2 (/ (pow (log (+ 1 (exp x))) 3) (pow y 3))) (* 6 (/ (pow (log (+ 1 (exp x))) 3) (pow y 3))))) x)) (* 1/2 (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2))) (* 2 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2)))))) x))) x)))) (taylor -inf x) (#s(alt (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) (patch (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ (log (/ -1 x)) (log (/ 1 y)))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (+ (log (/ -1 x)) (log (/ 1 y)))) (* -1 (/ (log (+ 1 (exp x))) (* x y)))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (+ (log (/ -1 x)) (log (/ 1 y)))) (* -1 (/ (+ (* 1/2 (/ (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2))) (* 2 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2)))) x)) (/ (log (+ 1 (exp x))) y)) x))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (+ (log (/ -1 x)) (log (/ 1 y)))) (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (+ (* -1 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2))) (* 2 (/ (pow (log (+ 1 (exp x))) 2) (pow y 2))))) (* 1/6 (/ (+ (* -6 (/ (pow (log (+ 1 (exp x))) 3) (pow y 3))) (+ (* -2 (/ (pow (log (+ 1 (exp x))) 3) (pow y 3))) (* 6 (/ (pow (log (+ 1 (exp x))) 3) (pow y 3))))) x))) x)) (/ (log (+ 1 (exp x))) y)) x))) (taylor -inf x) (#s(alt (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) (patch (.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ -1 (* x y)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (/ 1 y) (/ (log (+ 1 (exp x))) (* x (pow y 2)))) x)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow (log (+ 1 (exp x))) 2) (* x (pow y 3)))) (/ (log (+ 1 (exp x))) (pow y 2))) x)) (/ 1 y)) x)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow (log (+ 1 (exp x))) 3) (* x (pow y 4))) (* -1 (/ (pow (log (+ 1 (exp x))) 2) (pow y 3)))) x)) (/ (log (+ 1 (exp x))) (pow y 2))) x)) (/ 1 y)) x)) (taylor -inf x) (#s(alt (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) (patch (pow.f64 (fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x))) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log1p.f64 (exp.f64 x)) (patch (log1p.f64 (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log1p.f64 (exp.f64 x)) (patch (log1p.f64 (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log1p.f64 (exp.f64 x)) (patch (log1p.f64 (exp.f64 x)) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor -inf x) (#s(alt (log1p.f64 (exp.f64 x)) (patch (log1p.f64 (exp.f64 x)) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
13.0ms	x	@	-inf	((- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (neg y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (exp (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1)) (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1) (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1) (log (+ 1 (exp x))))
12.0ms	x	@	inf	((- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (neg y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (exp (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1)) (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1) (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1) (log (+ 1 (exp x))))
9.0ms	x	@	0	((- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (neg y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (exp (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1)) (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1) (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1) (log (+ 1 (exp x))))
7.0ms	y	@	0	((- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (neg y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (exp (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1)) (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1) (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1) (log (+ 1 (exp x))))
5.0ms	y	@	inf	((- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (neg y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (exp (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1)) (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) (* (log (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1)) -1) (pow (+ (* (neg y) x) (log (+ 1 (exp x)))) -1) (log (+ 1 (exp x))))

simplify206.0ms (3.1%)

Memory

2.9MiB live, 239.3MiB allocated

Algorithm

1×	egg-herbie

Rules

7 430×	`lower-fma.f64`
7 430×	`lower-fma.f32`
5 296×	`lower-*.f64`
5 296×	`lower-*.f32`
3 272×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	556	5464
1	1797	5032
2	6521	4967
0	8248	4383

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

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

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

rewrite158.0ms (2.4%)

Memory

-6.3MiB live, 235.2MiB allocated

Rules

4 614×	`lower-fma.f32`
4 604×	`lower-fma.f64`
3 964×	`lower-/.f64`
3 964×	`lower-/.f32`
3 556×	`lower-*.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	174
0	59	172
1	212	167
2	1461	163
0	8359	163

Stop Event

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

Counts

20 → 540

Calls

Call 1

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

Outputs
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eval260.0ms (3.9%)

Memory: 8.2MiB live, 277.6MiB allocated
Compiler: Compiled 24 471 to 3 080 computations (87.4% saved)

prune443.0ms (6.7%)

Memory

-1 091.0MiB live, 163.8MiB allocated

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	997	12	1 009
Fresh	2	2	4
Picked	4	1	5
Done	0	0	0
Total	1 003	15	1 018

Accuracy

99.7%

Counts

1 018 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	91.9%	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
	66.4%	(/.f64 (-.f64 (pow.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 y x) #s(literal 3 binary64))) (fma.f64 (.f64 y x) (fma.f64 y x (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))))
	68.1%	(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 (neg.f64 y) x #s(approx (log (+ 1 (exp x))) (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))))) #s(literal -1 binary64))) #s(literal -1 binary64)))
	55.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
▶	81.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))))
	52.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64))))
	27.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 (.f64 y y)) y) x))
▶	27.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (.f64 y y)))) x))
	27.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 (neg.f64 (*.f64 y y)) (/.f64 #s(literal 1 binary64) y)) x))
✓	48.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
	52.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))
	51.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
	86.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 (+.f64 (/.f64 (log.f64 #s(literal 2 binary64)) x) #s(literal 1/2 binary64)) y) x)))
▶	86.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))))
▶	35.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)))

Compiler

Compiled 315 to 269 computations (14.6% saved)

simplify118.0ms (1.8%)

Memory

-27.1MiB live, 106.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y))
cost-diff	0	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y)))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))))
cost-diff	1152	(*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))
cost-diff	0	#s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64))
cost-diff	0	(fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(fma.f64 (fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))))
cost-diff	0	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (.f64 y y)))) x)
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (.f64 y y)))) x))
cost-diff	448	(/.f64 y (neg.f64 (*.f64 y y)))
cost-diff	1280	(/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (*.f64 y y))))
cost-diff	0	(-.f64 #s(literal 1/2 binary64) y)
cost-diff	0	(*.f64 (-.f64 #s(literal 1/2 binary64) y) x)
cost-diff	0	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)))
cost-diff	0	#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
cost-diff	0	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
cost-diff	0	(neg.f64 y)
cost-diff	0	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))

Rules

7 572×	`lower-fma.f32`
7 564×	`lower-fma.f64`
2 730×	`lower-*.f32`
2 722×	`lower-*.f64`
1 242×	`lower--.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	304
0	65	298
1	112	294
2	199	283
3	575	280
4	1597	271
5	4587	271
0	8136	252

Stop Event

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

Calls

Call 1

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

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

localize112.0ms (1.7%)

Memory

1.5MiB live, 155.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.01171875	(-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y))
accuracy	0.13671875	(/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)
accuracy	3.6452074403047043	(*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))
accuracy	8.862767896624273	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))))
accuracy	0.0234375	(fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y))
accuracy	0.03125	(fma.f64 (fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))
accuracy	15.855591101671422	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))))
accuracy	19.44640287788234	#s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64))
accuracy	0	(neg.f64 (*.f64 y y))
accuracy	0.171875	(/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (*.f64 y y))))
accuracy	28.953050464232206	(/.f64 y (neg.f64 (*.f64 y y)))
accuracy	33.267802760363345	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (.f64 y y)))) x))
accuracy	0	(-.f64 #s(literal 1/2 binary64) y)
accuracy	0.0078125	(*.f64 (-.f64 #s(literal 1/2 binary64) y) x)
accuracy	8.862767896624273	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)))
accuracy	33.031893600224464	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))
accuracy	0	(neg.f64 y)
accuracy	0.01171875	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
accuracy	0.24598030713999228	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
accuracy	16.7297345430003	#s(approx (+ 1 (exp x)) #s(literal 2 binary64))

Samples

88.0ms

256×

valid

Compiler

Compiled 216 to 38 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 68.0ms

ival-mult: 35.0ms (51.5% of total)

ival-add: 8.0ms (11.8% of total)

ival-neg: 6.0ms (8.8% of total)

ival-div: 5.0ms (7.4% of total)

const: 4.0ms (5.9% of total)

ival-sub: 3.0ms (4.4% of total)

ival-log: 3.0ms (4.4% of total)

ival-log1p: 3.0ms (4.4% of total)

ival-exp: 2.0ms (2.9% of total)

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

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

exact: 0.0ms (0% of total)

series126.0ms (1.9%)

Memory

18.4MiB live, 212.0MiB allocated

Counts

22 → 432

Calls

Call 1

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

Outputs
#s(alt (log (+ 1 (exp x))) (taylor 0 y) (#s(alt (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (patch (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (patch (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (patch (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) (patch (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (* -1 y) (taylor 0 y) (#s(alt (neg.f64 y) (patch (neg.f64 y) #<representation binary64>) () ())) ())
#s(alt (log (+ 1 (exp x))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 #s(literal 1/2 binary64) y) x))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 #s(literal 1/2 binary64) y) x))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 #s(literal 1/2 binary64) y) x))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 #s(literal 1/2 binary64) y) x))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y)))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1/2 y)) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (neg.f64 y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* 1/2 (/ 1 y)) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (patch (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ 1 y)) (/ (log 2) (* x y))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (patch (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ 1 y)) (/ (log 2) (* x y))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (patch (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (+ (* 1/2 (/ 1 y)) (/ (log 2) (* x y))) 1))) (taylor -inf x) (#s(alt (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (patch (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
33.0ms	y	@	inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (+ 1 (exp x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ 1 (/ y (neg (* y y)))) (/ y (neg (* y y))) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ y (neg (* y y)))) x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg (* y y)) (/ (+ (* 1/2 x) (log 2)) y))
32.0ms	x	@	-inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (+ 1 (exp x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ 1 (/ y (neg (* y y)))) (/ y (neg (* y y))) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ y (neg (* y y)))) x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg (* y y)) (/ (+ (* 1/2 x) (log 2)) y))
17.0ms	y	@	0	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (+ 1 (exp x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ 1 (/ y (neg (* y y)))) (/ y (neg (* y y))) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ y (neg (* y y)))) x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg (* y y)) (/ (+ (* 1/2 x) (log 2)) y))
16.0ms	y	@	-inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (+ 1 (exp x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ 1 (/ y (neg (* y y)))) (/ y (neg (* y y))) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ y (neg (* y y)))) x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg (* y y)) (/ (+ (* 1/2 x) (log 2)) y))
9.0ms	x	@	inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (+ 1 (exp x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ 1 (/ y (neg (* y y)))) (/ y (neg (* y y))) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ y (neg (* y y)))) x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) x) (log 2)) (+ (* (+ (* (* x x) -1/192) 1/8) x) (- 1/2 y)) (+ (* (* x x) -1/192) 1/8) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg (* y y)) (/ (+ (* 1/2 x) (log 2)) y))

simplify123.0ms (1.8%)

Memory

12.3MiB live, 163.7MiB allocated

Algorithm

1×	egg-herbie

Rules

7 636×	`lower-fma.f64`
7 636×	`lower-fma.f32`
3 010×	`lower-*.f64`
3 010×	`lower-*.f32`
2 246×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	213	3632
1	665	3300
2	1873	3253
3	5948	3253
0	8309	2874

Stop Event

1×	iter limit
1×	node limit

Counts

432 → 430

Calls

Call 1

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

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

rewrite174.0ms (2.6%)

Memory

10.5MiB live, 217.5MiB allocated

Rules

5 638×	`lower-fma.f32`
5 630×	`lower-fma.f64`
4 522×	`lower-/.f32`
4 516×	`lower-/.f64`
3 940×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	269
0	65	263
1	250	259
2	1845	249
0	8662	233

Stop Event

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

Counts

22 → 599

Calls

Call 1

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

Outputs
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eval151.0ms (2.3%)

Memory: -10.7MiB live, 262.0MiB allocated
Compiler: Compiled 19 245 to 2 939 computations (84.7% saved)

prune105.0ms (1.6%)

Memory

1.4MiB live, 125.3MiB allocated

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	1 149	12	1 161
Fresh	4	5	9
Picked	3	2	5
Done	0	1	1
Total	1 156	20	1 176

Accuracy

99.7%

Counts

1 176 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	91.9%	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
	55.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
	56.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
	52.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64))))
	25.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 x (neg.f64 y)) (.f64 y y)))
	13.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 y))) (.f64 (.f64 y y) #s(literal 1 binary64))) (.f64 (.f64 y y) (neg.f64 (neg.f64 y))))) x))
	47.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x))
	27.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 (neg.f64 (*.f64 y y)) (/.f64 #s(literal 1 binary64) y)) x))
✓	48.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
	52.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))
▶	51.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
	38.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #s(literal 3 binary64))) (neg.f64 y)) (fma.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (+.f64 (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) x) (.f64 x x)))))
▶	20.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))))
▶	85.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))))
	41.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (exp.f64 (.f64 (neg.f64 (log.f64 (neg.f64 y))) #s(literal -1 binary64))))))
▶	91.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))) (neg.f64 y))))
✓	35.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)))
	35.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 #s(approx (- x (/ (+ ( 1/2 x) (log 2)) y)) (fma.f64 #s(literal -1/2 binary64) (/.f64 x y) x)) (neg.f64 y))))
	35.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 #s(approx (- 1/2 y) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) y)) x)))
▶	3.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)))

Compiler

Compiled 463 to 383 computations (17.3% saved)

simplify91.0ms (1.4%)

Memory

4.2MiB live, 78.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))))
cost-diff	1152	(*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))
cost-diff	1280	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))
cost-diff	0	(log.f64 #s(literal 2 binary64))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
cost-diff	0	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)
cost-diff	0	#s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))))
cost-diff	128	(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))
cost-diff	0	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
cost-diff	0	(*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)
cost-diff	0	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)))
cost-diff	0	(-.f64 x #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)))
cost-diff	0	#s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))) (neg.f64 y)))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))) (neg.f64 y))))
cost-diff	128	(.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))) (neg.f64 y))

Rules

3 806×	`lower-fma.f32`
3 804×	`lower-fma.f64`
1 778×	`lower-*.f32`
1 768×	`lower-*.f64`
1 452×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	380
0	65	368
1	103	368
2	174	368
3	411	365
4	1040	353
5	2466	353
6	4648	353
7	7288	353
0	8164	329

Stop Event

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

Calls

Call 1

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

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

localize100.0ms (1.5%)

Memory

-4.0MiB live, 127.3MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.13671875	(/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)
accuracy	0.171875	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))
accuracy	3.6452074403047043	(*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))
accuracy	8.862767896624273	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))))
accuracy	0	(log.f64 #s(literal 2 binary64))
accuracy	30.9121575978353	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
accuracy	6.122402699382292	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)
accuracy	6.7101151261834415	(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))
accuracy	8.862767896624273	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))))
accuracy	33.031893600224464	#s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))
accuracy	0.0078125	(*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)
accuracy	8.862767896624273	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)))
accuracy	33.031893600224464	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))
accuracy	34.83288946163259	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
accuracy	0.2109375	(/.f64 (log.f64 #s(literal 2 binary64)) y)
accuracy	3.6452074403047043	(.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))) (neg.f64 y))
accuracy	8.862767896624273	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))) (neg.f64 y))))
accuracy	19.951604321574298	#s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))

Samples

75.0ms

256×

valid

Compiler

Compiled 223 to 32 computations (85.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 48.0ms

ival-log1p: 14.0ms (29.3% of total)

ival-mult: 11.0ms (23% of total)

ival-div: 8.0ms (16.8% of total)

ival-sub: 4.0ms (8.4% of total)

ival-add: 3.0ms (6.3% of total)

ival-log: 3.0ms (6.3% of total)

ival-exp: 2.0ms (4.2% of total)

exact: 1.0ms (2.1% of total)

ival-neg: 1.0ms (2.1% of total)

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

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

series76.0ms (1.1%)

Memory

-25.5MiB live, 131.6MiB allocated

Counts

21 → 444

Calls

Call 1

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

Outputs
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#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))) #<representation binary64>) () ())) ())
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#s(alt (+ (* -1 (* x y)) (* 1/2 x)) (taylor 0 y) (#s(alt (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x y)) (* 1/2 x)) (taylor 0 y) (#s(alt (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (* x y)) (* 1/2 x)) (taylor 0 y) (#s(alt (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x) (patch (.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x) #<representation binary64>) () ())) ())
#s(alt 1/2 (taylor 0 y) (#s(alt #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (patch #s(approx (- 1/2 y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (patch #s(approx (- 1/2 y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (patch #s(approx (- 1/2 y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ 1/2 (* -1 y)) (taylor 0 y) (#s(alt #s(approx (- 1/2 y) #s(literal 1/2 binary64)) (patch #s(approx (- 1/2 y) #s(literal 1/2 binary64)) #<representation binary64>) () ())) ())
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#s(alt (log (+ 1 (exp x))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (+ (log (+ 1 (exp x))) (* -1 (* x y))) (taylor 0 y) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x y)) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1/2 y)) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) (patch #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) (patch #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) (patch #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) (patch #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (+.f64 #s(literal 1/2 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1/4 (pow y 2))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (patch (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1/4 (pow y 2))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (patch (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1/4 (pow y 2))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (patch (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #<representation binary64>) () ())) ())
#s(alt (* x (- 1/4 (pow y 2))) (taylor -inf x) (#s(alt (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) (patch (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) (patch #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (* y (- (* 1/2 (/ 1 y)) 1))) (taylor -inf x) (#s(alt (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) (patch (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* y (- (* 1/2 (/ 1 y)) 1))) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) (patch (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* y (- (* 1/2 (/ 1 y)) 1))) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) (patch (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (* y (- (* 1/2 (/ 1 y)) 1))) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) (patch (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x y)) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y)))) (taylor -inf x) (#s(alt #s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) (patch #s(approx (- (log (+ 1 (exp x))) ( x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))))) #<representation binary64>) () ())) ())
#s(alt (* x (- 1/2 y)) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))))) (taylor -inf x) (#s(alt #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) (patch #s(approx (+ ( (- 1/2 y) x) (log 2)) (*.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) (patch #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) (patch #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) (patch #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) (patch #s(approx (/ (+ (* 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) #<representation binary64>) () ())) ())
#s(alt (* 1/2 (/ x y)) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y))))) (taylor -inf x) (#s(alt (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) (patch (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y) #<representation binary64>) () ())) ())

Calls

6 calls:

Time	Variable		Point	Expression
19.0ms	y	@	0	((* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ (* (- 1/4 (* y y)) x) (+ 1/2 y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/4 (* y y)) x) (- (log (+ 1 (exp x))) (* x y)) (log 2) (/ 1 (/ -1 y)) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (/ 1 (/ -1 y))) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (/ (+ (* 1/2 x) (log 2)) y) (/ (log 2) y) (/ (+ (* 1/2 x) (log 2)) y))
14.0ms	y	@	-inf	((* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ (* (- 1/4 (* y y)) x) (+ 1/2 y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/4 (* y y)) x) (- (log (+ 1 (exp x))) (* x y)) (log 2) (/ 1 (/ -1 y)) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (/ 1 (/ -1 y))) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (/ (+ (* 1/2 x) (log 2)) y) (/ (log 2) y) (/ (+ (* 1/2 x) (log 2)) y))
11.0ms	y	@	inf	((* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ (* (- 1/4 (* y y)) x) (+ 1/2 y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/4 (* y y)) x) (- (log (+ 1 (exp x))) (* x y)) (log 2) (/ 1 (/ -1 y)) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (/ 1 (/ -1 y))) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (/ (+ (* 1/2 x) (log 2)) y) (/ (log 2) y) (/ (+ (* 1/2 x) (log 2)) y))
6.0ms	x	@	-inf	((* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ (* (- 1/4 (* y y)) x) (+ 1/2 y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/4 (* y y)) x) (- (log (+ 1 (exp x))) (* x y)) (log 2) (/ 1 (/ -1 y)) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (/ 1 (/ -1 y))) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (/ (+ (* 1/2 x) (log 2)) y) (/ (log 2) y) (/ (+ (* 1/2 x) (log 2)) y))
4.0ms	x	@	inf	((* (- x (/ (+ (* 1/2 x) (log 2)) y)) (neg y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- x (/ (+ (* 1/2 x) (log 2)) y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (/ (* (- 1/4 (* y y)) x) (+ 1/2 y)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/4 (* y y)) x) (- (log (+ 1 (exp x))) (* x y)) (log 2) (/ 1 (/ -1 y)) (* (- x (/ (+ (* 1/2 x) (log 2)) y)) (/ 1 (/ -1 y))) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (/ (+ (* 1/2 x) (log 2)) y) (/ (log 2) y) (/ (+ (* 1/2 x) (log 2)) y))

simplify133.0ms (2%)

Memory

38.5MiB live, 195.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 840×	`lower-fma.f64`
9 840×	`lower-fma.f32`
3 060×	`lower-*.f64`
3 060×	`lower-*.f32`
2 006×	`lower--.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	130	3843
1	390	3300
2	1071	3263
3	4343	3263
4	7308	3263
0	8103	2897

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 442

Calls

Call 1

Inputs
(+ (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)))
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(* -1 (* x (- (* -1 (/ (log 2) (* x y))) (* 1/2 (/ 1 y)))))

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

rewrite182.0ms (2.7%)

Memory

-23.5MiB live, 329.2MiB allocated

Rules

5 208×	`lower-/.f32`
5 198×	`lower-/.f64`
4 156×	`lower-*.f32`
4 146×	`lower-*.f64`
3 940×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	330
0	65	318
1	234	300
2	1674	300
0	8504	282

Stop Event

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

Counts

21 → 483

Calls

Call 1

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

Outputs
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eval133.0ms (2%)

Memory: 13.0MiB live, 213.3MiB allocated
Compiler: Compiled 16 864 to 2 480 computations (85.3% saved)

prune45.0ms (0.7%)

Memory

-7.2MiB live, 109.8MiB allocated

Pruning

22 alts after pruning (16 fresh and 6 done)

	Pruned	Kept	Total
New	924	5	929
Fresh	1	11	12
Picked	2	3	5
Done	0	3	3
Total	927	22	949

Accuracy

99.7%

Counts

949 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	91.9%	(fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))))
	55.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
	56.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(approx (+ (* (* x x) -1/192) 1/8) #s(literal 1/8 binary64)) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
	52.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64))))
	25.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 x (neg.f64 y)) (.f64 y y)))
	13.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 (neg.f64 y))) (.f64 (.f64 y y) #s(literal 1 binary64))) (.f64 (.f64 y y) (neg.f64 (neg.f64 y))))) x))
	47.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x))
	27.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (.f64 (neg.f64 (*.f64 y y)) (/.f64 #s(literal 1 binary64) y)) x))
✓	48.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
	52.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))
✓	51.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
	85.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (/.f64 #s(literal -1 binary64) y))))
	19.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (neg.f64 y) y) x)) (+.f64 #s(literal 1/2 binary64) y))))
	3.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x)) (+.f64 #s(literal 1/2 binary64) y))))
	41.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x (/.f64 (fma.f64 #s(literal 1/2 binary64) x (log.f64 #s(literal 2 binary64))) y)) (exp.f64 (.f64 (neg.f64 (log.f64 (neg.f64 y))) #s(literal -1 binary64))))))
✓	91.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y))) (neg.f64 y))))
	35.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (-.f64 x #s(approx (/ (+ ( 1/2 x) (log 2)) y) (*.f64 (/.f64 x y) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)))))
✓	35.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)))
	56.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (.f64 (-.f64 (.f64 x x) (pow.f64 #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(approx (/ (+ ( 1/2 x) (log 2)) y) (/.f64 (log.f64 #s(literal 2 binary64)) y)) x) (/.f64 #s(literal -1 binary64) y))))))
	35.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 #s(approx (- x (/ (+ ( 1/2 x) (log 2)) y)) (fma.f64 #s(literal -1/2 binary64) (/.f64 x y) x)) (neg.f64 y))))
	35.3%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 #s(approx (- 1/2 y) (.f64 (-.f64 (/.f64 #s(literal 1/2 binary64) y) #s(literal 1 binary64)) y)) x)))
✓	3.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)))

Compiler

Compiled 768 to 422 computations (45.1% saved)

regimes34.0ms (0.5%)

Memory

22.1MiB live, 65.8MiB allocated

Counts

39 → 1

Calls

Call 1

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

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

Calls

3 calls:

12.0ms	y
11.0ms	x
10.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

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

Compiler

Compiled 11 to 12 computations (-9.1% saved)

regimes28.0ms (0.4%)

Memory

-1.7MiB live, 37.4MiB allocated

Counts

31 → 2

Calls

Call 1

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

Outputs

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
99.5%	2	`x`
91.9%	1	`y`
97.8%	2	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 11 to 12 computations (-9.1% saved)

regimes10.0ms (0.1%)

Memory

-26.1MiB live, 12.8MiB allocated

Counts

26 → 2

Calls

Call 1

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

Outputs

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

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
99.5%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes8.0ms (0.1%)

Memory

10.9MiB live, 10.9MiB allocated

Counts

21 → 2

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes7.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

19 → 2

Calls

Call 1

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.4%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes7.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated

Counts

18 → 2

Calls

Call 1

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.4%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes12.0ms (0.2%)

Memory

-19.7MiB live, 19.4MiB allocated

Counts

17 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

2 calls:

6.0ms	x
5.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
96.9%	3	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
82.2%	2	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes6.0ms (0.1%)

Memory

12.6MiB live, 12.6MiB allocated

Counts

16 → 3

Calls

Call 1

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

Outputs

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

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

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

Calls

1 calls:

5.0ms

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

Results

Accuracy	Segments	Branch
96.3%	3	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes28.0ms (0.4%)

Memory

-7.7MiB live, 43.8MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

3 calls:

17.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
5.0ms	y
5.0ms	x

Results

Accuracy	Segments	Branch
48.0%	1	`x`
48.0%	1	`y`
48.0%	1	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 11 to 12 computations (-9.1% saved)

regimes31.0ms (0.5%)

Memory

-30.8MiB live, 8.5MiB 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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)))

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

Calls

3 calls:

28.0ms	x
1.0ms	y
1.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

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

Compiler

Compiled 11 to 12 computations (-9.1% saved)

bsearch12.0ms (0.2%)

Memory

12.8MiB live, 12.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	-9.45616311149435e+21	-223129866108283970.0

Samples

6.0ms

128×

valid

Compiler

Compiled 180 to 171 computations (5% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sub: 1.0ms (31.6% of total)

ival-exp: 1.0ms (31.6% of total)

ival-log1p: 1.0ms (31.6% of total)

ival-mult: 1.0ms (31.6% of total)

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

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

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-9.45616311149435e+21	-223129866108283970.0

Compiler

Compiled 140 to 147 computations (-5% saved)

bsearch1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-9.45616311149435e+21	-223129866108283970.0

Compiler

Compiled 116 to 131 computations (-12.9% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-9.45616311149435e+21	-223129866108283970.0

Compiler

Compiled 108 to 123 computations (-13.9% saved)

bsearch1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-9.45616311149435e+21	-223129866108283970.0

Compiler

Compiled 108 to 123 computations (-13.9% saved)

bsearch1.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.6933095512492722	691802.0542260373
0.0ms	1.0175914579981494e-37	0.6682015065498923

Compiler

Compiled 12 to 13 computations (-8.3% saved)

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.6933095512492722	691802.0542260373
0.0ms	1.0175914579981494e-37	0.6682015065498923

Compiler

Compiled 12 to 13 computations (-8.3% saved)

simplify32.0ms (0.5%)

Memory

6.1MiB live, 45.3MiB allocated

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative-binary64-+.f64`
12×	`-commutative-binary64-.f64`
12×	`sub-neg-binary64-neg.f64-+.f64--.f64`
6×	`neg-sub0-binary64--.f64-neg.f64`
6×	`neg-mul-1-binary64-*.f64-neg.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	358
1	81	358
2	91	358
3	96	358
4	98	358

Stop Event

1×

saturated

Calls

Call 1

Inputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x)) (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) (-.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 4789048565205903/23945242826029513411849172299223580994042798784118784 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 (neg.f64 y) x)) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64)))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 4789048565205903/23945242826029513411849172299223580994042798784118784 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 (neg.f64 y) x)) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)))

Outputs
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
(-.f64 (log.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) (*.f64 y x))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 (fma.f64 (fma.f64 (*.f64 x x) #s(literal -1/192 binary64) #s(literal 1/8 binary64)) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x)) (fma.f64 (neg.f64 y) x (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 x y)))
(if (<=.f64 x #s(literal -230000000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (neg.f64 y) x)) (-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (.f64 y x)))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 4789048565205903/23945242826029513411849172299223580994042798784118784 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 (neg.f64 y) x)) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64)))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) (.f64 y x)) #s(literal 4789048565205903/23945242826029513411849172299223580994042798784118784 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 (neg.f64 y) x)) (if (<=.f64 (-.f64 (log.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) (.f64 y x)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64)))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 4789048565205903/23945242826029513411849172299223580994042798784118784 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 (neg.f64 y) x)) (if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) (.f64 y x)) #s(literal 4789048565205903/23945242826029513411849172299223580994042798784118784 binary64)) #s(approx (- (log (+ 1 (exp x))) ( x y)) (.f64 (neg.f64 y) x)) (if (<=.f64 (-.f64 (log.f64 (+.f64 (exp.f64 x) #s(literal 1 binary64))) (.f64 y x)) #s(literal 1 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)))

soundness1.3s (18.9%)

Memory

-21.4MiB live, 580.4MiB allocated

Rules

11 474×	`lower-fma.f64`
11 474×	`lower-fma.f32`
7 636×	`lower-fma.f64`
7 636×	`lower-fma.f32`
7 430×	`lower-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	213	3632
1	665	3300
2	1873	3253
3	5948	3253
0	8309	2874
0	67	385
1	180	370
2	389	370
3	1351	370
4	4010	370
5	6711	370
0	8052	300
0	556	5464
1	1797	5032
2	6521	4967
0	8248	4383
0	36	174
0	59	172
1	212	167
2	1461	163
0	8359	163

Stop Event

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

Compiler

Compiled 309 to 166 computations (46.3% saved)

preprocess92.0ms (1.4%)

Memory: 34.0MiB live, 111.7MiB allocated
Compiler: Compiled 454 to 156 computations (65.6% 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

start0.0ms (0%)

analyze66.0ms (1%)

sample1.1s (16.8%)

explain94.0ms (1.4%)

preprocess39.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify10.0ms (0.1%)

localize116.0ms (1.7%)

series58.0ms (0.9%)

simplify121.0ms (1.8%)

rewrite159.0ms (2.4%)

eval64.0ms (1%)

prune13.0ms (0.2%)

simplify295.0ms (4.4%)

localize141.0ms (2.1%)

series64.0ms (1%)

simplify206.0ms (3.1%)

rewrite158.0ms (2.4%)

eval260.0ms (3.9%)

prune443.0ms (6.7%)

simplify118.0ms (1.8%)

localize112.0ms (1.7%)

series126.0ms (1.9%)

simplify123.0ms (1.8%)

rewrite174.0ms (2.6%)

eval151.0ms (2.3%)

prune105.0ms (1.6%)

simplify91.0ms (1.4%)

localize100.0ms (1.5%)

series76.0ms (1.1%)

simplify133.0ms (2%)

rewrite182.0ms (2.7%)

eval133.0ms (2%)

prune45.0ms (0.7%)

regimes34.0ms (0.5%)

regimes28.0ms (0.4%)

regimes10.0ms (0.1%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

regimes12.0ms (0.2%)

regimes6.0ms (0.1%)

regimes28.0ms (0.4%)

regimes31.0ms (0.5%)

bsearch12.0ms (0.2%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify32.0ms (0.5%)

soundness1.3s (18.9%)

preprocess92.0ms (1.4%)

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