Metrics for Logistic regression 2

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze68.0ms (1.2%)

Memory

21.4MiB live, 99.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
50%	50%	50%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
75%	74.9%	25%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
75%	74.9%	25%	0.1%	0%	0%	0%	7
75%	74.9%	25%	0.1%	0%	0%	0%	8
75%	74.9%	25%	0.1%	0%	0%	0%	9
75%	74.9%	25%	0.1%	0%	0%	0%	10
75%	74.9%	25%	0.1%	0%	0%	0%	11
75%	74.9%	25%	0.1%	0%	0%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.4s (24.1%)

Memory

21.2MiB live, 1 118.7MiB allocated

Samples

723.0ms	8 256×	0	valid
220.0ms	2 600×	1	exit

Precisions

Click to see histograms. Total time spent on operations: 602.0ms

ival-log1p: 194.0ms (32.2% of total)

ival-exp: 156.0ms (25.9% of total)

ival-mult: 144.0ms (23.9% of total)

ival-sub: 55.0ms (9.1% of total)

adjust: 41.0ms (6.8% of total)

ival-true: 9.0ms (1.5% of total)

ival-assert: 4.0ms (0.7% of total)

Bogosity

explain100.0ms (1.8%)

Memory

-14.4MiB live, 147.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
2	78	(-1.2496975866047165e+132 3.5051553852756226e+87)	-	`(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	78	0
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))`	oflow-rescue	2	0
↳	`(exp.f64 x)`	overflow	2
↳	`(+.f64 #s(literal 1 binary64) (exp.f64 x))`	overflow	2

Confusion

	Predicted +	Predicted -
+	2	0
-	78	176

Precision

0.025

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	78	0	176

Precision?

0.025

Recall?

1.0

Freqs

test

number	freq
0	176
1	80

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

36.0ms

512×

valid

Compiler

Compiled 65 to 28 computations (56.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-log1p: 6.0ms (28.9% of total)

ival-mult: 5.0ms (24.1% of total)

ival-exp: 4.0ms (19.3% of total)

ival-sub: 2.0ms (9.6% of total)

ival-add: 2.0ms (9.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess29.0ms (0.5%)

Memory

-2.5MiB live, 36.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	51
1	58	49
2	121	49
3	235	49
4	322	49
5	446	49
6	502	49
7	547	49
8	551	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	163	9
8	213	9
9	240	9
10	264	9
11	273	9
0	273	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: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 9 to 8 computations (11.1% saved)

simplify9.0ms (0.2%)

Memory

11.4MiB live, 11.4MiB 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	2	(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

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	163	26
8	213	26
9	240	26
10	264	26
11	273	26
0	273	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

localize26.0ms (0.5%)

Memory

-5.6MiB live, 35.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x y)
accuracy	0.0	(exp.f64 x)
accuracy	0.0078125	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
accuracy	0.4841415752782323	(log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x)))

Samples

19.0ms

256×

valid

Compiler

Compiled 28 to 10 computations (64.3% saved)

Precisions

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

ival-log1p: 3.0ms (31.1% of total)

ival-exp: 2.0ms (20.7% of total)

ival-mult: 2.0ms (20.7% of total)

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

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

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

exact: 0.0ms (0% of total)

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

series56.0ms (1%)

Memory

0.6MiB live, 76.7MiB allocated

Counts

5 → 25

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)
(*.f64 x y)

Outputs
(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) (* 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))))))
(* x y)
(log (+ 1 (exp x)))
(* -1 (* x y))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(+ 1 (exp x))
(exp x)
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))

Calls

6 calls:

Time	Variable		Point	Expression
28.0ms	x	@	inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x) (* x y))
21.0ms	x	@	-inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x) (* x y))
3.0ms	y	@	0	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x) (* x y))
1.0ms	y	@	-inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x) (* x y))
1.0ms	y	@	inf	((log (+ 1 (exp x))) (- (log (+ 1 (exp x))) (* x y)) (+ 1 (exp x)) (exp x) (* x y))

simplify122.0ms (2.2%)

Memory

11.0MiB live, 127.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	197
1	180	197
2	399	197
3	1386	197
4	4230	187
5	7018	187
0	8031	153

Stop Event

1×	iter limit
1×	node limit

Counts

25 → 25

Calls

Call 1

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

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

rewrite175.0ms (3.1%)

Memory

-26.3MiB live, 216.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
0	13	23
1	47	23
2	311	23
3	2719	23
0	9082	19

Stop Event

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

Counts

5 → 368

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)
(*.f64 x y)

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

eval47.0ms (0.8%)

Memory: -1.5MiB live, 81.1MiB allocated
Compiler: Compiled 13 339 to 1 491 computations (88.8% saved)

prune7.0ms (0.1%)

Memory

23.7MiB live, 23.7MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	384	5	389
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	385	5	390

Accuracy

99.7%

Counts

390 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
▶	93.8%	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
▶	82.3%	#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))))
▶	87.8%	#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))

Compiler

Compiled 138 to 114 computations (17.4% saved)

simplify60.0ms (1.1%)

Memory

-2.7MiB live, 36.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	141
0	44	141
1	71	141
2	99	141
3	195	141
4	329	141
5	568	141
6	954	141
7	1626	141
8	1984	141
9	2134	141
10	2134	141
0	2134	141

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize61.0ms (1.1%)

Memory

0.3MiB live, 82.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	(log.f64 #s(literal 2 binary64))
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64)))
accuracy	11.329339931910383	#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))))
accuracy	0.0	(fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64)))
accuracy	0.0	(-.f64 #s(literal 1/2 binary64) y)
accuracy	0.0	(log.f64 #s(literal 2 binary64))
accuracy	7.806339204726264	#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	0.0	(*.f64 x y)
accuracy	0.0078125	(-.f64 (log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64))) (*.f64 x y))
accuracy	0.4841415752782323	(log.f64 #s(approx (+ 1 (exp x)) #s(literal 2 binary64)))
accuracy	17.101488200569694	#s(approx (+ 1 (exp x)) #s(literal 2 binary64))
accuracy	0.0	(*.f64 (neg.f64 y) x)
accuracy	0.0	(neg.f64 y)
accuracy	33.30034131022919	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
accuracy	0.0	(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
accuracy	0.0	(neg.f64 y)
accuracy	0.0	(exp.f64 x)
accuracy	0.4880478252782323	(log1p.f64 (exp.f64 x))

Samples

45.0ms

256×

valid

Compiler

Compiled 128 to 24 computations (81.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-mult: 8.0ms (27.9% of total)

ival-add: 6.0ms (20.9% of total)

ival-log: 5.0ms (17.4% of total)

ival-log1p: 4.0ms (13.9% of total)

ival-exp: 2.0ms (7% of total)

ival-sub: 2.0ms (7% of total)

ival-neg: 1.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.6%)

Memory

7.6MiB live, 44.2MiB allocated

Counts

17 → 59

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
12.0ms	x	@	inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)))
8.0ms	x	@	-inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)))
4.0ms	x	@	0	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)))
4.0ms	y	@	0	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)))
3.0ms	y	@	inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (* (neg y) x) (- (log (+ 1 (exp x))) (* x y)) (log (+ 1 (exp x))) (+ 1 (exp x)) (* x y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)))

simplify147.0ms (2.6%)

Memory

-2.6MiB live, 112.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	485
1	494	483
2	1333	483
3	4978	457
0	8390	386

Stop Event

1×	iter limit
1×	node limit

Counts

59 → 59

Calls

Call 1

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

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

rewrite203.0ms (3.6%)

Memory

-8.7MiB live, 186.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	118
0	44	118
1	163	118
2	1197	118
0	8292	118

Stop Event

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

Counts

17 → 343

Calls

Call 1

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

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

eval59.0ms (1%)

Memory: -5.8MiB live, 114.6MiB allocated
Compiler: Compiled 14 406 to 1 532 computations (89.4% saved)

prune14.0ms (0.2%)

Memory

33.4MiB live, 33.4MiB allocated

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	432	9	441
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	434	12	446

Accuracy

99.7%

Counts

446 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
▶	93.9%	(fma.f64 (neg.f64 y) x (log1p.f64 #s(approx (exp x) #s(literal 1 binary64))))
	57.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
✓	87.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64))))
▶	53.1%	#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))))
▶	29.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (.f64 y y)))) x))
	29.7%	#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))
▶	36.8%	#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)))
▶	31.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x)))
	7.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
	52.7%	#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))

Compiler

Compiled 410 to 329 computations (19.8% saved)

simplify120.0ms (2.1%)

Memory

-26.1MiB live, 88.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(log.f64 #s(literal 2 binary64))
cost-diff	0	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64)))
cost-diff	0	#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))))
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	3	(/.f64 y (neg.f64 (*.f64 y y)))
cost-diff	3	(/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (*.f64 y y))))
cost-diff	0	(fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y))
cost-diff	0	(*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x)
cost-diff	0	#s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x)))
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 (exp x) #s(literal 1 binary64))
cost-diff	0	(log1p.f64 #s(approx (exp x) #s(literal 1 binary64)))
cost-diff	0	(neg.f64 y)
cost-diff	0	(fma.f64 (neg.f64 y) x (log1p.f64 #s(approx (exp x) #s(literal 1 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	235
0	59	229
1	98	225
2	166	214
3	482	214
4	1033	214
5	2511	214
6	4883	214
7	7837	214
0	8440	202

Stop Event

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

Calls

Call 1

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

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

localize79.0ms (1.4%)

Memory

-3.1MiB live, 80.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x (log.f64 #s(literal 2 binary64)))
accuracy	0.0	(log.f64 #s(literal 2 binary64))
accuracy	7.806339204726264	#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))))
accuracy	33.555714675934894	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
accuracy	0.0	(neg.f64 (*.f64 y y))
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (*.f64 y y))))
accuracy	29.70476231857823	(/.f64 y (neg.f64 (*.f64 y y)))
accuracy	33.30034131022919	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 #s(literal 1 binary64) (/.f64 y (neg.f64 (.f64 y y)))) x))
accuracy	0.0	(-.f64 #s(literal 1/2 binary64) y)
accuracy	0.015625	(*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x)
accuracy	11.329339931910383	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x)))
accuracy	33.025620349897466	#s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x))
accuracy	0.0	(-.f64 #s(literal 1/2 binary64) y)
accuracy	0.00390625	(*.f64 (-.f64 #s(literal 1/2 binary64) y) x)
accuracy	7.806339204726264	#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	33.13522453758681	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x))
accuracy	0.0	(fma.f64 (neg.f64 y) x (log1p.f64 #s(approx (exp x) #s(literal 1 binary64))))
accuracy	0.0	(neg.f64 y)
accuracy	0.4880478252782323	(log1p.f64 #s(approx (exp x) #s(literal 1 binary64)))
accuracy	20.17354613916671	#s(approx (exp x) #s(literal 1 binary64))

Samples

48.0ms

256×

valid

Compiler

Compiled 164 to 28 computations (82.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 11.0ms (34% of total)

ival-add: 4.0ms (12.4% of total)

ival-div: 3.0ms (9.3% of total)

ival-log: 3.0ms (9.3% of total)

ival-log1p: 3.0ms (9.3% of total)

ival-neg: 3.0ms (9.3% of total)

ival-exp: 2.0ms (6.2% of total)

ival-sub: 2.0ms (6.2% of total)

exact: 1.0ms (3.1% of total)

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

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

series34.0ms (0.6%)

Memory

5.5MiB live, 43.9MiB allocated

Counts

21 → 64

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
8.0ms	x	@	inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (* (+ (* 1/8 x) (- 1/2 y)) x) (+ (* 1/8 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)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (neg (* y y)))
8.0ms	x	@	-inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (* (+ (* 1/8 x) (- 1/2 y)) x) (+ (* 1/8 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)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (neg (* y y)))
7.0ms	y	@	inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (* (+ (* 1/8 x) (- 1/2 y)) x) (+ (* 1/8 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)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (neg (* y y)))
4.0ms	y	@	0	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (* (+ (* 1/8 x) (- 1/2 y)) x) (+ (* 1/8 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)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (neg (* y y)))
3.0ms	y	@	-inf	((+ (* (neg y) x) (log (+ 1 (exp x)))) (neg y) (log (+ 1 (exp x))) (exp x) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (* (+ (* 1/8 x) (- 1/2 y)) x) (+ (* 1/8 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)) (+ (* (- 1/2 y) x) (log 2)) (- 1/2 y) (log 2) (neg (* y y)))

simplify181.0ms (3.2%)

Memory

5.6MiB live, 85.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	172	504
1	545	504
2	1510	504
3	5623	484
0	8391	413

Stop Event

1×	iter limit
1×	node limit

Counts

64 → 64

Calls

Call 1

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

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

rewrite154.0ms (2.7%)

Memory

20.8MiB live, 129.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	213
0	59	207
1	215	203
2	1543	192
0	8496	180

Stop Event

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

Counts

21 → 474

Calls

Call 1

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

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

eval98.0ms (1.7%)

Memory: -6.1MiB live, 119.5MiB allocated
Compiler: Compiled 17 227 to 2 110 computations (87.8% saved)

prune21.0ms (0.4%)

Memory

10.1MiB live, 48.1MiB allocated

Pruning

19 alts after pruning (13 fresh and 6 done)

	Pruned	Kept	Total
New	513	9	522
Fresh	0	4	4
Picked	2	3	5
Done	0	3	3
Total	515	19	534

Accuracy

99.7%

Counts

534 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
✓	93.9%	(fma.f64 (neg.f64 y) x (log1p.f64 #s(approx (exp x) #s(literal 1 binary64))))
▶	57.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
✓	87.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64))))
✓	53.1%	#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))))
▶	47.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
	47.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) y) x)))
	27.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
▶	47.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x))
	29.7%	#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))
	22.7%	#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))))
▶	22.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)))))
	24.2%	#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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.f64 #s(literal 1/2 binary64) y))) x)))
✓	36.8%	#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)))
▶	3.6%	#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)))
	7.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
	7.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
	52.7%	#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))

Compiler

Compiled 700 to 544 computations (22.3% saved)

simplify208.0ms (3.7%)

Memory

-18.2MiB live, 66.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	#s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x))))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)))))
cost-diff	1	(/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x))
cost-diff	2	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)))
cost-diff	0	(/.f64 #s(literal -1 binary64) y)
cost-diff	0	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x)
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x))
cost-diff	3	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))
cost-diff	0	(/.f64 #s(literal -1 binary64) y)
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
cost-diff	1	(/.f64 x (/.f64 #s(literal -1 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	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
cost-diff	0	(fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64)))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64)))
cost-diff	0	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	272
0	55	266
1	90	261
2	148	255
3	351	255
4	641	255
5	1141	255
6	1544	255
7	2237	255
8	2887	255
9	4080	255
10	5940	255
11	6521	255
12	6619	255
13	6647	255
14	6666	255
15	7179	255
16	7720	255
0	8281	237

Stop Event

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

Calls

Call 1

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

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

localize74.0ms (1.3%)

Memory

12.0MiB live, 87.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	5.17826713950312	(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)
accuracy	6.820010994712883	(/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x))
accuracy	7.806339204726264	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)))))
accuracy	33.13522453758681	#s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x))))
accuracy	0.0	(/.f64 #s(literal -1 binary64) y)
accuracy	0.0	(*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x)
accuracy	0.15234375	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y))
accuracy	33.30034131022919	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x))
accuracy	0.0	(/.f64 #s(literal -1 binary64) y)
accuracy	0.17578125	(/.f64 x (/.f64 #s(literal -1 binary64) y))
accuracy	33.30034131022919	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
accuracy	0.00390625	(*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x)
accuracy	7.806339204726264	#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	33.13522453758681	#s(approx (+ (* (- 1/2 y) x) (log 2)) (*.f64 #s(approx (- 1/2 y) #s(literal 1/2 binary64)) x))
accuracy	33.555714675934894	#s(approx (- 1/2 y) #s(literal 1/2 binary64))
accuracy	0.0	(log.f64 #s(literal 2 binary64))
accuracy	0.0078125	(fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64)))
accuracy	11.329339931910383	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
accuracy	33.555714675934894	#s(approx (- 1/2 y) #s(literal 1/2 binary64))

Samples

54.0ms

256×

valid

Compiler

Compiled 178 to 32 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 11.0ms (30.3% of total)

ival-div: 8.0ms (22% of total)

ival-add: 5.0ms (13.8% of total)

ival-sub: 4.0ms (11% of total)

ival-log: 3.0ms (8.3% of total)

ival-log1p: 3.0ms (8.3% of total)

ival-exp: 2.0ms (5.5% of total)

exact: 1.0ms (2.8% of total)

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

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

series44.0ms (0.8%)

Memory

-5.2MiB live, 39.5MiB allocated

Counts

19 → 62

Calls

Call 1

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

Outputs
(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)
(* x (- 1/2 y))
(* -1 (* x y))
(/ (* x (- 1/4 (pow y 2))) (+ 1/2 y))
(/ (+ 1/2 y) (* x (- 1/4 (pow y 2))))
(* x (- 1/4 (pow y 2)))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* 1/8 (pow x 2))
(* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))
(* 1/8 x)
(* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))
(* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(+ 1/2 (* 1/8 x))
(+ 1/2 (+ (* -1 y) (* 1/8 x)))
1/2
(+ 1/2 (* -1 y))
(+ (log 2) (* 1/2 x))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(* 1/2 x)
(+ (* -1 (* x y)) (* 1/2 x))
(/ -1 y)
(* -1 y)
(/ 2 x)
(+ (* 4 (/ y x)) (* 2 (/ 1 x)))
(+ (* y (+ (* 8 (/ y x)) (* 4 (/ 1 x)))) (* 2 (/ 1 x)))
(+ (* y (+ (* y (+ (* 16 (/ y x)) (* 8 (/ 1 x)))) (* 4 (/ 1 x)))) (* 2 (/ 1 x)))
(* 1/4 x)
(+ (* -1 (* x (pow y 2))) (* 1/4 x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (* 1/2 (/ x y))))
(/ -1 (* x y))
(* -1 (/ (+ (/ 1 x) (* 1/2 (/ 1 (* x y)))) y))
(/ (- (* -1 (/ (+ (* 1/2 (/ 1 x)) (* 1/4 (/ 1 (* x y)))) y)) (/ 1 x)) y)
(/ (- (* -1 (/ (+ (* 1/4 (/ 1 x)) (* 1/8 (/ 1 (* x y)))) (pow y 2))) (+ (/ 1/2 (* x y)) (/ 1 x))) y)
(* -1 (* x (pow y 2)))
(* (pow y 2) (+ (* -1 x) (* 1/4 (/ x (pow y 2)))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1/2 (/ x y)))))
(* -1 (/ (+ (/ 1/4 (* x (pow y 2))) (+ (/ 1/2 (* x y)) (/ 1 x))) y))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/4 (/ 1 x)) (* 1/8 (/ 1 (* x y)))) y)) (* 1/2 (/ 1 x))) y)) (/ 1 x)) y))

Calls

6 calls:

Time	Variable		Point	Expression
23.0ms	x	@	-inf	((- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (/ x (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (/ -1 y) (/ 1 (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ -1 y)) x) (/ 1 (/ (+ 1/2 y) (* (- 1/4 (* y y)) x))) (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (log 2) (* (- 1/4 (* y y)) x))
5.0ms	y	@	0	((- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (/ x (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (/ -1 y) (/ 1 (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ -1 y)) x) (/ 1 (/ (+ 1/2 y) (* (- 1/4 (* y y)) x))) (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (log 2) (* (- 1/4 (* y y)) x))
4.0ms	x	@	inf	((- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (/ x (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (/ -1 y) (/ 1 (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ -1 y)) x) (/ 1 (/ (+ 1/2 y) (* (- 1/4 (* y y)) x))) (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (log 2) (* (- 1/4 (* y y)) x))
4.0ms	y	@	inf	((- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (/ x (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (/ -1 y) (/ 1 (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ -1 y)) x) (/ 1 (/ (+ 1/2 y) (* (- 1/4 (* y y)) x))) (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (log 2) (* (- 1/4 (* y y)) x))
4.0ms	x	@	0	((- (log (+ 1 (exp x))) (* x y)) (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (+ (* 1/8 x) (- 1/2 y)) (- 1/2 y) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (* (- 1/2 y) x) (/ x (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (/ -1 y) (/ 1 (/ -1 y)) (- (log (+ 1 (exp x))) (* x y)) (* (/ 1 (/ -1 y)) x) (/ 1 (/ (+ 1/2 y) (* (- 1/4 (* y y)) x))) (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (- (log (+ 1 (exp x))) (* x y)) (+ (* (- 1/2 y) x) (log 2)) (log 2) (* (- 1/4 (* y y)) x))

simplify152.0ms (2.7%)

Memory

9.9MiB live, 162.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	200	618
1	598	601
2	1682	591
3	6787	585
0	8248	544

Stop Event

1×	iter limit
1×	node limit

Counts

62 → 62

Calls

Call 1

Inputs
(log 2)
(+ (log 2) (* x (- 1/2 y)))
(+ (log 2) (* x (- (+ 1/2 (* 1/8 x)) y)))
(+ (log 2) (* x (- (+ 1/2 (* x (+ 1/8 (* -1/192 (pow x 2))))) y)))
(- 1/2 y)
(- (+ 1/2 (* 1/8 x)) y)
(* x (- 1/2 y))
(* -1 (* x y))
(/ (* x (- 1/4 (pow y 2))) (+ 1/2 y))
(/ (+ 1/2 y) (* x (- 1/4 (pow y 2))))
(* x (- 1/4 (pow y 2)))
(* x (- (/ (log (+ 1 (exp x))) x) y))
(* 1/8 (pow x 2))
(* (pow x 2) (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* (pow x 2) (- (+ 1/8 (+ (* 1/2 (/ 1 x)) (/ (log 2) (pow x 2)))) (/ y x)))
(* 1/8 x)
(* x (- (+ 1/8 (* 1/2 (/ 1 x))) (/ y x)))
(* x (- (+ 1/2 (/ (log 2) x)) y))
(* -1 (* x (- (* -1 (/ (log (+ 1 (exp x))) x)) (* -1 y))))
(* (pow x 2) (+ 1/8 (* -1 (/ (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x))) x))))
(* -1 (* x (- (* -1 (/ (- 1/2 y) x)) 1/8)))
(* -1 (* x (+ (* -1 (- 1/2 y)) (* -1 (/ (log 2) x)))))
(log (+ 1 (exp x)))
(+ (log (+ 1 (exp x))) (* -1 (* x y)))
(+ (log 2) (* x (+ 1/2 (* 1/8 x))))
(+ (log 2) (+ (* -1 (* x y)) (* x (+ 1/2 (* 1/8 x)))))
(+ 1/2 (* 1/8 x))
(+ 1/2 (+ (* -1 y) (* 1/8 x)))
1/2
(+ 1/2 (* -1 y))
(+ (log 2) (* 1/2 x))
(+ (log 2) (+ (* -1 (* x y)) (* 1/2 x)))
(* 1/2 x)
(+ (* -1 (* x y)) (* 1/2 x))
(/ -1 y)
(* -1 y)
(/ 2 x)
(+ (* 4 (/ y x)) (* 2 (/ 1 x)))
(+ (* y (+ (* 8 (/ y x)) (* 4 (/ 1 x)))) (* 2 (/ 1 x)))
(+ (* y (+ (* y (+ (* 16 (/ y x)) (* 8 (/ 1 x)))) (* 4 (/ 1 x)))) (* 2 (/ 1 x)))
(* 1/4 x)
(+ (* -1 (* x (pow y 2))) (* 1/4 x))
(* y (- (/ (log (+ 1 (exp x))) y) x))
(* y (+ (* -1 x) (+ (/ (log 2) y) (/ (* x (+ 1/2 (* 1/8 x))) y))))
(* y (- (+ (* 1/8 (/ x y)) (* 1/2 (/ 1 y))) 1))
(* y (- (* 1/2 (/ 1 y)) 1))
(* y (+ (* -1 x) (+ (* 1/2 (/ x y)) (/ (log 2) y))))
(* y (+ (* -1 x) (* 1/2 (/ x y))))
(/ -1 (* x y))
(* -1 (/ (+ (/ 1 x) (* 1/2 (/ 1 (* x y)))) y))
(/ (- (* -1 (/ (+ (* 1/2 (/ 1 x)) (* 1/4 (/ 1 (* x y)))) y)) (/ 1 x)) y)
(/ (- (* -1 (/ (+ (* 1/4 (/ 1 x)) (* 1/8 (/ 1 (* x y)))) (pow y 2))) (+ (/ 1/2 (* x y)) (/ 1 x))) y)
(* -1 (* x (pow y 2)))
(* (pow y 2) (+ (* -1 x) (* 1/4 (/ x (pow y 2)))))
(* -1 (* y (- (* -1 (/ (log (+ 1 (exp x))) y)) (* -1 x))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* x (+ 1/2 (* 1/8 x)))) y)))))
(* -1 (* y (+ 1 (* -1 (/ (+ 1/2 (* 1/8 x)) y)))))
(* -1 (* y (- 1 (* 1/2 (/ 1 y)))))
(* -1 (* y (+ x (* -1 (/ (+ (log 2) (* 1/2 x)) y)))))
(* -1 (* y (+ x (* -1/2 (/ x y)))))
(* -1 (/ (+ (/ 1/4 (* x (pow y 2))) (+ (/ 1/2 (* x y)) (/ 1 x))) y))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (* 1/4 (/ 1 x)) (* 1/8 (/ 1 (* x y)))) y)) (* 1/2 (/ 1 x))) y)) (/ 1 x)) y))

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

rewrite216.0ms (3.8%)

Memory

-4.3MiB live, 194.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	235
0	55	229
1	207	196
2	1383	196
0	8449	182

Stop Event

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

Counts

19 → 416

Calls

Call 1

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

Outputs
#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
(.f64 (-.f64 (pow.f64 (log.f64 #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (log.f64 #s(literal 2 binary64)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x))))
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(.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64))) x) (pow.f64 (fma.f64 (*.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 x (-.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (fma.f64 y y #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 x (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64)))) (pow.f64 (fma.f64 (*.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 y y)) x) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)
(.f64 #s(literal -1 binary64) (.f64 (neg.f64 x) (-.f64 #s(literal 1/4 binary64) (*.f64 y y))))
(.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y)))
(.f64 #s(literal 1 binary64) (.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 y y)) x))
(pow.f64 (pow.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 #s(literal 1/4 binary64) x)) (.f64 (.f64 (.f64 (neg.f64 y) y) x) (.f64 (.f64 (neg.f64 y) y) x))) (-.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (neg.f64 y) y) x)))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 (.f64 x (.f64 (neg.f64 y) y)) (.f64 x (.f64 (neg.f64 y) y)))) (-.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x (*.f64 (neg.f64 y) y))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 1/4 binary64) x) #s(literal 3 binary64)) (pow.f64 (.f64 (.f64 (neg.f64 y) y) x) #s(literal 3 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 #s(literal 1/4 binary64) x) (-.f64 (.f64 (.f64 (.f64 (neg.f64 y) y) x) (.f64 (.f64 (neg.f64 y) y) x)) (.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (.f64 (neg.f64 y) y) x)))))
(/.f64 (+.f64 (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 (neg.f64 y) y)) #s(literal 3 binary64))) (fma.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x (.f64 (neg.f64 y) y)) (.f64 x (.f64 (neg.f64 y) y))) (.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x (.f64 (neg.f64 y) y))))))
(/.f64 (neg.f64 (*.f64 (-.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 4 binary64))) x)) (neg.f64 (fma.f64 y y #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64))) x)) (neg.f64 (fma.f64 (.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64))))
(/.f64 (neg.f64 (*.f64 x (-.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (fma.f64 y y #s(literal 1/4 binary64))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64))))) (neg.f64 (fma.f64 (.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 4 binary64))) x) (fma.f64 y y #s(literal 1/4 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64))) x) (fma.f64 (.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64)))
(/.f64 (*.f64 x (-.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 y y #s(literal 1/4 binary64)))
(/.f64 (.f64 x (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64)))
(/.f64 (.f64 (neg.f64 x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #s(literal 1 binary64))
(/.f64 x (pow.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 y y)) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 1/4 binary64)) (*.f64 (-.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 4 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64)) (.f64 (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64))) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 y y #s(literal 1/4 binary64)) (*.f64 x (-.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 y y) (fma.f64 y y #s(literal 1/4 binary64)) #s(literal 1/16 binary64)) (.f64 x (-.f64 #s(literal 1/64 binary64) (pow.f64 y #s(literal 6 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x) #s(literal -1 binary64)))
(neg.f64 (.f64 (neg.f64 x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))))
(fma.f64 #s(literal 1/4 binary64) x (.f64 (.f64 (neg.f64 y) y) x))
(fma.f64 x (.f64 (neg.f64 y) y) (.f64 x #s(literal 1/4 binary64)))
(fma.f64 x #s(literal 1/4 binary64) (.f64 x (.f64 (neg.f64 y) y)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) x) (.f64 #s(literal 1 binary64) (.f64 (.f64 (neg.f64 y) y) x)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64)) (.f64 #s(literal 1 binary64) (.f64 x (.f64 (neg.f64 y) y))))
(-.f64 #s(literal 0 binary64) (.f64 (neg.f64 x) (-.f64 #s(literal 1/4 binary64) (.f64 y y))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (*.f64 y y)) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) x)) (.f64 #s(literal 1 binary64) (.f64 (*.f64 (neg.f64 y) y) x)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))) (.f64 #s(literal 1 binary64) (.f64 x (*.f64 (neg.f64 y) y))))
(+.f64 (.f64 #s(literal 1/4 binary64) x) (.f64 (*.f64 (neg.f64 y) y) x))
(+.f64 (.f64 x (.f64 (neg.f64 y) y)) (*.f64 x #s(literal 1/4 binary64)))
(+.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 x (*.f64 (neg.f64 y) y)))

eval76.0ms (1.4%)

Memory: -2.8MiB live, 72.8MiB allocated
Compiler: Compiled 15 902 to 1 993 computations (87.5% saved)

prune29.0ms (0.5%)

Memory

11.5MiB live, 57.9MiB allocated

Pruning

28 alts after pruning (18 fresh and 10 done)

	Pruned	Kept	Total
New	446	13	459
Fresh	3	5	8
Picked	0	5	5
Done	1	5	6
Total	450	28	478

Accuracy

99.7%

Counts

478 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	93.9%	(fma.f64 (neg.f64 y) x (log1p.f64 #s(approx (exp x) #s(literal 1 binary64))))
✓	57.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x (log.f64 #s(literal 2 binary64))))
✓	87.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (fma.f64 (-.f64 #s(literal 1/2 binary64) y) x (log.f64 #s(literal 2 binary64))))
✓	53.1%	#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))))
	47.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
✓	47.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
	47.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal -1 binary64) y) x)))
	27.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
✓	47.9%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) y)) x))
✓	48.0%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))
	53.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log1p.f64 (exp.f64 x)))
	52.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) (log.f64 #s(literal 2 binary64)))
	22.7%	#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))))
✓	22.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) x)))))
	26.1%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
	26.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
	2.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
	36.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 1/2 binary64) y) x)))))
	47.8%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
	36.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
	3.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
	9.2%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.f64 #s(literal 1/2 binary64) y)))))
✓	36.8%	#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)))
✓	3.6%	#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)))
	36.7%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
	7.4%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
	23.6%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x x))))
	7.5%	#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))

Compiler

Compiled 1 629 to 744 computations (54.3% saved)

regimes39.0ms (0.7%)

Memory

-16.9MiB live, 56.7MiB allocated

Counts

37 → 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))
#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 (log1p.f64 #s(approx (exp x) #s(literal 1 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(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)) (log1p.f64 (exp.f64 x)))
(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Outputs
(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))

Calls

3 calls:

14.0ms	x
13.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))
11.0ms	y

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	1	`y`
99.2%	1	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 11 to 12 computations (-9.1% saved)

regimes32.0ms (0.6%)

Memory

19.5MiB live, 57.9MiB allocated

Counts

35 → 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))
#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 (log1p.f64 #s(approx (exp x) #s(literal 1 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(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)) (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 #s(literal 1/8 binary64) x (-.f64 #s(literal 1/2 binary64) y)) x (log.f64 #s(literal 2 binary64))))

Calls

3 calls:

11.0ms	y
10.0ms	x
9.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

Results

Accuracy	Segments	Branch
99.3%	2	`x`
93.9%	1	`y`
98.4%	2	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 11 to 12 computations (-9.1% saved)

regimes14.0ms (0.3%)

Memory

-25.0MiB live, 20.6MiB allocated

Counts

33 → 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))
#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 (log1p.f64 #s(approx (exp x) #s(literal 1 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(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:

13.0ms

Results

Accuracy	Segments	Branch
99.2%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes11.0ms (0.2%)

Memory

17.8MiB live, 17.8MiB 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))
#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 (log1p.f64 #s(approx (exp x) #s(literal 1 binary64))))

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

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
99.0%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes12.0ms (0.2%)

Memory

-21.1MiB live, 17.0MiB allocated

Counts

30 → 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))
#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:

9.0ms

Results

Accuracy	Segments	Branch
99.0%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes18.0ms (0.3%)

Memory

28.2MiB live, 28.2MiB allocated

Counts

29 → 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))
#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:

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

Results

Accuracy	Segments	Branch
97.2%	3	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
85.1%	3	`x`

Compiler

Compiled 10 to 10 computations (0% saved)

regimes11.0ms (0.2%)

Memory

-22.7MiB live, 15.0MiB allocated

Counts

28 → 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))
#s(approx (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))
#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 (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64)))

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

Calls

1 calls:

10.0ms

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

Results

Accuracy	Segments	Branch
97.1%	3	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`

Compiler

Compiled 9 to 8 computations (11.1% saved)

regimes26.0ms (0.5%)

Memory

0.6MiB live, 38.2MiB allocated

Counts

26 → 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 (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (.f64 x x) #s(literal 1/8 binary64))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x #s(approx (- 1/2 y) #s(literal 1/2 binary64))) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (*.f64 (fma.f64 #s(literal 1/8 binary64) x (-.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 #s(literal 2 binary64) x)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 x (/.f64 #s(literal -1 binary64) y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 y (/.f64 #s(literal -1 binary64) x)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (.f64 (/.f64 (neg.f64 x) y) (.f64 y y)))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) #s(approx (* (- 1/2 y) x) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x (neg.f64 x)) y))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (+ (* 1/8 x) (- 1/2 y)) x) (log 2)) (.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) y) x) #s(literal -1/8 binary64)) (.f64 x 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)) (*.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.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(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (*.f64 #s(literal 1/4 binary64) x))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (/.f64 #s(literal -1 binary64) x) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) (/.f64 #s(literal 1 binary64) (/.f64 (/.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 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (neg.f64 y) (.f64 y x)))))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.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)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (.f64 (/.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 y y))) (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 y y)) (-.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 #s(literal 1/2 binary64) y)) (/.f64 (.f64 y y) (+.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(literal 1 binary64) #s(approx (/ (+ 1/2 y) (* (- 1/4 (* y y)) x)) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal -1/2 binary64) y) x) (/.f64 #s(literal 1 binary64) x)) y)))))
#s(approx (- (log (+ 1 (exp x))) (* x y)) #s(approx (+ (* (- 1/2 y) x) (log 2)) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) y) #s(approx (* (- 1/4 (* y y)) x) (.f64 (.f64 (fma.f64 (/.f64 (/.f64 x y) y) #s(literal 1/4 binary64) (neg.f64 x)) y) y))))))

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

Calls

3 calls:

10.0ms	x
8.0ms	y
7.0ms	(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))

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)

regimes4.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB 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:

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

Results

Accuracy	Segments	Branch
3.6%	1	`(-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (*.f64 x y))`
3.6%	1	`x`
3.6%	1	`y`

Compiler

Compiled 11 to 12 computations (-9.1% saved)

bsearch4.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	-15581068522121.473	-13870167019184.842

Samples

2.0ms

32×

valid

Compiler

Compiled 80 to 69 computations (13.8% saved)

Precisions

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

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

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

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

ival-log1p: 0.0ms (0% of total)

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

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

bsearch1.0ms (0%)

Memory

1.0MiB live, 1.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	-15581068522121.473	-13870167019184.842

Compiler

Compiled 74 to 65 computations (12.2% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	-15581068522121.473	-13870167019184.842

Compiler

Compiled 58 to 53 computations (8.6% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	-15581068522121.473	-13870167019184.842

Compiler

Compiled 62 to 57 computations (8.1% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.6931943661364949	3.042114808952302
0.0ms	9.070105762555997e-9	0.6928945750993275

Compiler

Compiled 12 to 13 computations (-8.3% saved)

bsearch1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	0.6931943661364949	3.042114808952302
0.0ms	9.070105762555997e-9	0.6928945750993275

Compiler

Compiled 12 to 13 computations (-8.3% saved)

simplify113.0ms (2%)

Memory

-1.7MiB live, 38.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	285
1	97	285
2	127	285
3	169	285
4	215	285
5	327	285
6	1436	285
7	3880	285
8	7535	285

Stop Event

1×	node limit

Calls

Call 1

Inputs
(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
(if (<=.f64 x #s(literal -14000000000000 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 -14000000000000 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 -14000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x)) (fma.f64 (neg.f64 y) x (log1p.f64 #s(approx (exp x) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal -14000000000000 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 3022314549036573/302231454903657293676544 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 3022314549036573/302231454903657293676544 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 (+ (* (neg y) x) (log (+ 1 (exp x)))) (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
(fma.f64 (neg.f64 y) x (log1p.f64 (exp.f64 x)))
(if (<=.f64 x #s(literal -14000000000000 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 -14000000000000 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 -14000000000000 binary64)) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x)) (fma.f64 (neg.f64 y) x (log1p.f64 #s(approx (exp x) #s(literal 1 binary64)))))
(if (<=.f64 x #s(literal -14000000000000 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 3022314549036573/302231454903657293676544 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 (or (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 3022314549036573/302231454903657293676544 binary64)) (not (<=.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)) (.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)))))
(if (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 3022314549036573/302231454903657293676544 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 (+ (* (neg y) x) (log (+ 1 (exp x)))) (log.f64 #s(literal 2 binary64))) #s(approx (- (log (+ 1 (exp x))) (* x y)) (*.f64 (neg.f64 y) x))))
(if (or (<=.f64 (-.f64 (log.f64 (+.f64 #s(literal 1 binary64) (exp.f64 x))) (.f64 x y)) #s(literal 3022314549036573/302231454903657293676544 binary64)) (not (<=.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)) (.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))
#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)))

soundness1.2s (21.3%)

Memory

-19.7MiB live, 523.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	23
0	13	23
1	47	23
2	311	23
3	2719	23
0	9082	19
0	159	485
1	494	483
2	1333	483
3	4978	457
0	8390	386
0	172	504
1	545	504
2	1510	504
3	5623	484
0	8391	413
0	67	197
1	180	197
2	399	197
3	1386	197
4	4230	187
5	7018	187
0	8031	153

Stop Event

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

Compiler

Compiled 470 to 204 computations (56.6% saved)

preprocess89.0ms (1.6%)

Memory: -16.3MiB live, 102.1MiB allocated
Compiler: Compiled 640 to 174 computations (72.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	22	51
1	58	49
2	121	49
3	235	49
4	322	49
5	446	49
6	502	49
7	547	49
8	551	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	163	9
8	213	9
9	240	9
10	264	9
11	273	9
0	273	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	163	26
8	213	26
9	240	26
10	264	26
11	273	26
0	273	22

Iter	Nodes	Cost
0	22	51
1	58	49
2	121	49
3	235	49
4	322	49
5	446	49
6	502	49
7	547	49
8	551	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	163	9
8	213	9
9	240	9
10	264	9
11	273	9
0	273	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	163	26
8	213	26
9	240	26
10	264	26
11	273	26
0	273	22

start0.0ms (0%)

analyze68.0ms (1.2%)

sample1.4s (24.1%)

explain100.0ms (1.8%)

preprocess29.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.2%)

localize26.0ms (0.5%)

series56.0ms (1%)

simplify122.0ms (2.2%)

rewrite175.0ms (3.1%)

eval47.0ms (0.8%)

prune7.0ms (0.1%)

simplify60.0ms (1.1%)

localize61.0ms (1.1%)

series35.0ms (0.6%)

simplify147.0ms (2.6%)

rewrite203.0ms (3.6%)

eval59.0ms (1%)

prune14.0ms (0.2%)

simplify120.0ms (2.1%)

localize79.0ms (1.4%)

series34.0ms (0.6%)

simplify181.0ms (3.2%)

rewrite154.0ms (2.7%)

eval98.0ms (1.7%)

prune21.0ms (0.4%)

simplify208.0ms (3.7%)

localize74.0ms (1.3%)

series44.0ms (0.8%)

simplify152.0ms (2.7%)

rewrite216.0ms (3.8%)

eval76.0ms (1.4%)

prune29.0ms (0.5%)

regimes39.0ms (0.7%)

regimes32.0ms (0.6%)

regimes14.0ms (0.3%)

regimes11.0ms (0.2%)

regimes12.0ms (0.2%)

regimes18.0ms (0.3%)

regimes11.0ms (0.2%)

regimes26.0ms (0.5%)

regimes4.0ms (0.1%)

bsearch4.0ms (0.1%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

bsearch1.0ms (0%)

simplify113.0ms (2%)

soundness1.2s (21.3%)

preprocess89.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	22	51
1	58	49
2	121	49
3	235	49
4	322	49
5	446	49
6	502	49
7	547	49
8	551	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	163	9
8	213	9
9	240	9
10	264	9
11	273	9
0	273	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	163	26
8	213	26
9	240	26
10	264	26
11	273	26
0	273	22