Metrics for ln(1 + x)

analyze1.0ms (0%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
83.3%	62.5%	12.5%	0%	0%	25%	0%	4
91.7%	68.7%	6.2%	0%	0%	25%	0%	5
95.8%	71.8%	3.1%	0%	0%	25%	0%	6
97.9%	73.4%	1.6%	0%	0%	25%	0%	7
99%	74.2%	0.8%	0%	0%	25%	0%	8
99.5%	74.6%	0.4%	0%	0%	25%	0%	9
99.7%	74.8%	0.2%	0%	0%	25%	0%	10
99.9%	74.9%	0.1%	0%	0%	25%	0%	11
99.9%	74.9%	0%	0%	0%	25%	0%	12

Compiler

Compiled 6 to 4 computations (33.3% saved)

sample355.0ms (9.1%)

Memory

26.8MiB live, 445.4MiB allocated

Samples

214.0ms	8 256×	0	valid
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 85.0ms

ival-log1p: 76.0ms (89.8% of total)

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

ival-assert: 3.0ms (3.5% of total)

Bogosity

preprocess16.0ms (0.4%)

Memory

-19.6MiB live, 17.2MiB allocated

Algorithm

2×	egg-herbie

Rules

20×	`sub-neg`
14×	`+-commutative`
10×	`associate-+l-`
8×	`associate--r+`
6×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	18	13
2	25	13
3	33	13
4	43	13
5	56	13
6	72	13
7	76	13
0	4	4
1	7	4
0	7	2

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(log (+ 1 x))

Outputs
(log (+ 1 x))
(log1p.f64 x)

Call 2

Inputs
(log (+ 1 x))
(log (+ 1 (neg x)))
(neg (log (+ 1 (neg x))))

Outputs
(log (+ 1 x))
(log (+ 1 (neg x)))
(log (- 1 x))
(neg (log (+ 1 (neg x))))
(neg (log (- 1 x)))

explain48.0ms (1.2%)

Memory

27.3MiB live, 70.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
177	-	1	(-0.015443205929312954)	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
0	-	0	-	`(+.f64 #s(literal 1 binary64) x)`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`log.f64`	`(log.f64 (+.f64 #s(literal 1 binary64) x))`	sensitivity	176	1

Confusion

	Predicted +	Predicted -
+	176	1
-	0	79

Precision

1.0

Recall

0.9943502824858758

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	176	1	0
-	0	0	79

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	80
1	176

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

18.0ms

512×

valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-log1p: 5.0ms (61.6% of total)

ival-add: 3.0ms (36.9% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	36.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

-34.0MiB live, 3.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Rules

4×	`+-lowering-+.f64`
4×	`+-lowering-+.f32`
2×	`accelerator-lowering-log1p.f32`
2×	`log-lowering-log.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
1	7	9
0	7	7

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(log (+ 1 x))
(+ 1 x)
1
x

Outputs
(log (+ 1 x))
(log1p.f64 x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x

localize14.0ms (0.4%)

Memory

26.0MiB live, 26.0MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	36.4%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Samples

9.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

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

ival-log1p: 2.0ms (48.4% of total)

ival-add: 1.0ms (24.2% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated

Counts

2 → 24

Calls

Call 1

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

Outputs
#s(alt x (taylor 0 x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* -1/2 x))) (taylor 0 x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* 1/3 x) 1/2)))) (taylor 0 x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2)))) (taylor 0 x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (log (/ 1 x))) (taylor inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (* -1 (log (/ 1 x))) (/ 1 x)) (taylor inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2))) (taylor inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2))) (taylor inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (* -1 (log (/ -1 x)))) (taylor -inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x))) (taylor -inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x)))) (taylor -inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x)))) (taylor -inf x) (#s(alt (log (+ 1 x)) (patch (log.f64 (+.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt 1 (taylor 0 x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (+ 1 x) (taylor 0 x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt x (taylor -inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (+ 1 x) (patch (+.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())

Calls

6 calls:

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

rewrite338.0ms (8.6%)

Memory

10.8MiB live, 405.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 606×	`accelerator-lowering-fma.f32`
6 606×	`accelerator-lowering-fma.f64`
4 022×	`/-lowering-/.f32`
4 022×	`/-lowering-/.f64`
3 648×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	20	7
2	129	7
3	980	7
0	8596	5

Stop Event

1×	iter limit
1×	node limit

Counts

2 → 344

Calls

Call 1

Inputs
(log (+ 1 x))
(+ 1 x)

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

simplify978.0ms (25%)

Memory

-14.3MiB live, 515.0MiB allocated

Algorithm

1×	egg-herbie

Rules

17 822×	`accelerator-lowering-fma.f32`
17 822×	`accelerator-lowering-fma.f64`
2 868×	`+-lowering-+.f64`
2 868×	`+-lowering-+.f32`
2 630×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	169
1	171	155
2	363	150
3	980	148
4	2419	144
5	4413	144
6	5329	144
7	6636	144
8	7416	144
9	7564	144
10	7608	144
11	7610	144
12	7610	144
13	7853	144
14	7970	144
15	7978	144
16	7986	144
17	7986	144
0	8425	138

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 24

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))

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

eval84.0ms (2.1%)

Memory: 19.9MiB live, 91.3MiB allocated
Compiler: Compiled 11 134 to 1 115 computations (90% saved)

prune66.0ms (1.7%)

Memory

-28.6MiB live, 131.9MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	363	5	368
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	364	5	369

Accuracy

100.0%

Counts

369 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	69.3%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (*.f64 x x) x)
▶	70.2%	(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)
▶	68.9%	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
▶	100.0%	(log1p.f64 x)
▶	69.6%	x

Compiler

Compiled 70 to 42 computations (40% saved)

simplify28.0ms (0.7%)

Memory

24.5MiB live, 63.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64))
✓	cost-diff	(fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))
✓	cost-diff	(fma.f64 (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (*.f64 x x) x)
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64))
✓	cost-diff	(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)
✓	cost-diff	(*.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
✓	cost-diff	(log1p.f64 x)

Rules

1 072×	`accelerator-lowering-fma.f32`
1 072×	`accelerator-lowering-fma.f64`
340×	`-lowering-.f32`
340×	`-lowering-.f64`
232×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	76
1	47	76
2	86	76
3	174	76
4	385	76
5	460	76
6	591	76
7	592	76
0	592	64

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize66.0ms (1.7%)

Memory

6.1MiB live, 153.7MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64))
✓	accuracy	99.9%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (*.f64 x x) x)
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)
✓	accuracy	99.8%	(fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
✓	accuracy	100.0%	(*.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(log1p.f64 x)

Samples

44.0ms

256×

valid

Compiler

Compiled 66 to 21 computations (68.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 16.0ms (50.9% of total)

ival-add: 6.0ms (19.1% of total)

const: 6.0ms (19.1% of total)

ival-log1p: 3.0ms (9.6% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.3%)

Memory

-36.4MiB live, 24.2MiB allocated

Counts

9 → 108

Calls

Call 1

Inputs
#s(alt (log (+ 1 x)) (patch (log1p.f64 x) #<representation binary64>) () ())
#s(alt (+ (* x (* x -1/2)) x) (patch (fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x) #<representation binary64>) () ())
#s(alt (* x -1/2) (patch (*.f64 x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (+ (* (+ (* x 1/3) -1/2) (* x x)) x) (patch (fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x) #<representation binary64>) () ())
#s(alt (+ (* x 1/3) -1/2) (patch (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (* x x) (patch (*.f64 x x) #<representation binary64>) () ())
#s(alt (+ (* (+ (* x (+ (* x -1/4) 1/3)) -1/2) (* x x)) x) (patch (fma.f64 (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (*.f64 x x) x) #<representation binary64>) () ())
#s(alt (+ (* x (+ (* x -1/4) 1/3)) -1/2) (patch (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (+ (* x -1/4) 1/3) (patch (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #<representation binary64>) () ())

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

Calls

27 calls:

Time	Variable		Point	Expression
6.0ms	x	@	inf	(+ (* (+ (* x (+ (* x -1/4) 1/3)) -1/2) (* x x)) x)
1.0ms	x	@	-inf	(+ (* (+ (* x 1/3) -1/2) (* x x)) x)
0.0ms	x	@	0	(+ (* x (* x -1/2)) x)
0.0ms	x	@	inf	(+ (* x (* x -1/2)) x)
0.0ms	x	@	inf	(+ (* (+ (* x 1/3) -1/2) (* x x)) x)

rewrite441.0ms (11.3%)

Memory

7.6MiB live, 675.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 642×	`accelerator-lowering-fma.f32`
6 642×	`accelerator-lowering-fma.f64`
4 832×	`-lowering-.f32`
4 832×	`-lowering-.f64`
4 352×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	62
1	129	62
2	1022	62
0	8331	50

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 322

Calls

Call 1

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

Outputs
(log.f64 (+.f64 #s(literal 1 binary64) x))
(+.f64 (log1p.f64 (.f64 x (.f64 x x))) (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(+.f64 (log1p.f64 (.f64 x (.f64 x x))) (neg.f64 (log1p.f64 (-.f64 (*.f64 x x) x))))
(+.f64 (log1p.f64 (neg.f64 (*.f64 x x))) (log.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(+.f64 (log1p.f64 (neg.f64 (*.f64 x x))) (neg.f64 (log1p.f64 (neg.f64 x))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(-.f64 (log1p.f64 (.f64 x (.f64 x x))) (log1p.f64 (-.f64 (*.f64 x x) x)))
(-.f64 (log1p.f64 (.f64 x (.f64 x x))) (log.f64 (fma.f64 x x (-.f64 #s(literal 1 binary64) x))))
(-.f64 (log1p.f64 (neg.f64 (*.f64 x x))) (log1p.f64 (neg.f64 x)))
(-.f64 (log.f64 (neg.f64 (fma.f64 x (*.f64 x x) #s(literal 1 binary64)))) (log.f64 (neg.f64 (fma.f64 x (+.f64 x #s(literal -1 binary64)) #s(literal 1 binary64)))))
(-.f64 (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (log.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(-.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) (log.f64 (+.f64 x #s(literal -1 binary64))))
(neg.f64 (log.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (.f64 x (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (log1p.f64 (-.f64 (.f64 x x) x)) #s(literal 3 binary64))) (fma.f64 (log1p.f64 (.f64 x (.f64 x x))) (log1p.f64 (.f64 x (.f64 x x))) (fma.f64 (log1p.f64 (-.f64 (.f64 x x) x)) (log1p.f64 (-.f64 (.f64 x x) x)) (.f64 (log1p.f64 (.f64 x (.f64 x x))) (log1p.f64 (-.f64 (*.f64 x x) x))))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (neg.f64 (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (log1p.f64 (neg.f64 x)) #s(literal 3 binary64))) (fma.f64 (log1p.f64 (neg.f64 (.f64 x x))) (log1p.f64 (neg.f64 (.f64 x x))) (fma.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x)) (.f64 (log1p.f64 (neg.f64 (*.f64 x x))) (log1p.f64 (neg.f64 x))))))
(/.f64 (-.f64 (.f64 (log1p.f64 (.f64 x (.f64 x x))) (log1p.f64 (.f64 x (.f64 x x)))) (.f64 (log1p.f64 (-.f64 (.f64 x x) x)) (log1p.f64 (-.f64 (.f64 x x) x)))) (+.f64 (log1p.f64 (.f64 x (.f64 x x))) (log1p.f64 (-.f64 (*.f64 x x) x))))
(/.f64 (-.f64 (.f64 (log1p.f64 (neg.f64 (.f64 x x))) (log1p.f64 (neg.f64 (.f64 x x)))) (.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 (neg.f64 x)))) (+.f64 (log1p.f64 (neg.f64 (*.f64 x x))) (log1p.f64 (neg.f64 x))))
(log1p.f64 x)
(+.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) x))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)) (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (-.f64 x (.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
(fma.f64 #s(literal 1 binary64) x (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 x #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
(fma.f64 #s(literal -1/2 binary64) (*.f64 x x) x)
(fma.f64 (*.f64 x #s(literal -1/2 binary64)) x x)
(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
(fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 #s(literal -1/2 binary64) (.f64 x x)) x)) (neg.f64 (/.f64 (.f64 x x) (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) x))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (.f64 x x)))
(neg.f64 (/.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64)))) (neg.f64 (fma.f64 x (-.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64)))))))
(neg.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (.f64 x x)) (neg.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (*.f64 x x)) x))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 x (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal -1/8 binary64))))) (fma.f64 x (-.f64 x (.f64 #s(literal -1/2 binary64) (.f64 x x))) (.f64 (.f64 x x) (.f64 (*.f64 x x) #s(literal 1/4 binary64))))))
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(/.f64 (-.f64 (.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64)) #s(literal 1/9 binary64))) (*.f64 (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal -1/262144 binary64) #s(literal 1/19683 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/4096 binary64) (-.f64 #s(literal 1/729 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal -1/1728 binary64)))) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal 1/9 binary64)) (.f64 x #s(literal 1/12 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/4096 binary64) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64) #s(literal -1/27 binary64)) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal 1/9 binary64)) (*.f64 x #s(literal 1/12 binary64)))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/4096 binary64) #s(literal -1/729 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/256 binary64) (+.f64 #s(literal 1/81 binary64) (.f64 (.f64 x x) #s(literal 1/144 binary64)))) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))))
(/.f64 (.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x x)) #s(literal 1/256 binary64) #s(literal -1/81 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal 1/9 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64) #s(literal 1/27 binary64)))) (neg.f64 (neg.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal 1/9 binary64)) (.f64 x #s(literal 1/12 binary64))))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (*.f64 x x) #s(literal 1/16 binary64) #s(literal -1/9 binary64)))) (neg.f64 (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/3 binary64))))
(/.f64 (neg.f64 (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/16 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/3 binary64) (*.f64 x #s(literal -1/4 binary64)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (/.f64 #s(literal 1/9 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (fma.f64 (/.f64 #s(literal 1/9 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (.f64 (/.f64 (.f64 (*.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64)))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64)))) (.f64 (/.f64 #s(literal 1/9 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))))) (+.f64 (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64))) (/.f64 #s(literal 1/9 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal -1/3 binary64)))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal 1/9 binary64)) (*.f64 x #s(literal 1/12 binary64)))))
(.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64) #s(literal 1/27 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/9 binary64) (fma.f64 (.f64 x x) #s(literal 1/16 binary64) (*.f64 x #s(literal 1/12 binary64))))))
(.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal -1/9 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/3 binary64))))
(.f64 (neg.f64 (fma.f64 (.f64 x (.f64 x x)) #s(literal -1/64 binary64) #s(literal 1/27 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal 1/9 binary64)) (*.f64 x #s(literal 1/12 binary64))))))
(.f64 (neg.f64 (fma.f64 (.f64 x x) #s(literal 1/16 binary64) #s(literal -1/9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x #s(literal 1/4 binary64) #s(literal 1/3 binary64))))
(.f64 (+.f64 #s(literal 1/9 binary64) (.f64 #s(literal -1/16 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 x #s(literal -1/4 binary64)))))

simplify433.0ms (11%)

Memory

37.3MiB live, 456.1MiB allocated

Algorithm

1×	egg-herbie

Rules

9 064×	`accelerator-lowering-fma.f32`
9 064×	`accelerator-lowering-fma.f64`
2 638×	`-lowering-.f32`
2 638×	`-lowering-.f64`
1 860×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	108	713
1	297	698
2	773	686
3	2466	676
4	6230	672
0	8098	603

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1 (log (/ 1 x)))
(+ (* -1 (log (/ 1 x))) (/ 1 x))
(- (+ (* -1 (log (/ 1 x))) (/ 1 x)) (/ 1/2 (pow x 2)))
(- (+ (* -1 (log (/ 1 x))) (+ (/ 1 x) (* 1/3 (/ 1 (pow x 3))))) (/ 1/2 (pow x 2)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (/ 1 x)))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* 1/2 (/ 1 x)) 1) x))))
(+ (log -1) (+ (* -1 (log (/ -1 x))) (* -1 (/ (- (* -1 (/ (- (* 1/3 (/ 1 x)) 1/2) x)) 1) x))))
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* -1/2 x)))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* -1/2 (pow x 2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* (pow x 2) (- (/ 1 x) 1/2))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* 1/3 (pow x 3))
(* (pow x 3) (- 1/3 (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* (pow x 3) (- (+ 1/3 (/ 1 (pow x 2))) (* 1/2 (/ 1 x))))
(* 1/3 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3)))
-1/2
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(- (* 1/3 x) 1/2)
(* 1/3 x)
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* x (- 1/3 (* 1/2 (/ 1 x))))
(* 1/3 x)
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(* -1 (* x (- (* 1/2 (/ 1 x)) 1/3)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* -1/2 x)))
(* x (+ 1 (* x (- (* 1/3 x) 1/2))))
(* x (+ 1 (* x (- (* x (+ 1/3 (* -1/4 x))) 1/2))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 4) (- (+ (* 1/3 (/ 1 x)) (/ 1 (pow x 3))) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 4))
(* (pow x 4) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 4) (- (* -1 (/ (- (* -1 (/ (- (/ 1 x) 1/2) x)) 1/3) x)) 1/4))
-1/2
(- (* 1/3 x) 1/2)
(- (* x (+ 1/3 (* -1/4 x))) 1/2)
(- (* x (+ 1/3 (* -1/4 x))) 1/2)
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* (pow x 2) (- (* 1/3 (/ 1 x)) (+ 1/4 (/ 1/2 (pow x 2)))))
(* -1/4 (pow x 2))
(* (pow x 2) (- (* 1/3 (/ 1 x)) 1/4))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
(* (pow x 2) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/3) x)) 1/4))
1/3
(+ 1/3 (* -1/4 x))
(+ 1/3 (* -1/4 x))
(+ 1/3 (* -1/4 x))
(* -1/4 x)
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* x (- (* 1/3 (/ 1 x)) 1/4))
(* -1/4 x)
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))
(* -1 (* x (- 1/4 (* 1/3 (/ 1 x)))))

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

eval63.0ms (1.6%)

Memory: 9.8MiB live, 173.5MiB allocated
Compiler: Compiled 12 743 to 1 186 computations (90.7% saved)

prune80.0ms (2%)

Memory

0.2MiB live, 158.4MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	450	0	450
Fresh	0	0	0
Picked	0	5	5
Done	0	0	0
Total	450	5	455

Accuracy

100.0%

Counts

455 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	69.3%	(fma.f64 (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (*.f64 x x) x)
✓	70.2%	(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)
✓	68.9%	(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
✓	100.0%	(log1p.f64 x)
✓	69.6%	x

Compiler

Compiled 70 to 37 computations (47.1% saved)

regimes33.0ms (0.8%)

Memory

-23.1MiB live, 16.7MiB allocated

Counts

6 → 1

Calls

Call 1

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

Outputs
(log1p.f64 x)

Calls

3 calls:

27.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
3.0ms	x
2.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
100.0%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes6.0ms (0.1%)

Memory

16.7MiB live, 16.7MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
x
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)
(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)
(fma.f64 (fma.f64 x (fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64)) #s(literal -1/2 binary64)) (*.f64 x x) x)

Outputs
(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)

Calls

3 calls:

2.0ms	x
2.0ms	(+.f64 #s(literal 1 binary64) x)
2.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
70.2%	1	`x`
70.2%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
70.2%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

regimes5.0ms (0.1%)

Memory

-25.3MiB live, 13.9MiB allocated

Accuracy

Total -0.9b remaining (-4.6%)

Threshold costs -0.9b (-4.6%)

Counts

2 → 1

Calls

Call 1

Inputs
x
(fma.f64 x (*.f64 x #s(literal -1/2 binary64)) x)

Outputs
x

Calls

3 calls:

2.0ms	x
1.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))
1.0ms	(+.f64 #s(literal 1 binary64) x)

Results

Accuracy	Segments	Branch
69.6%	1	`x`
69.6%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
69.6%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify7.0ms (0.2%)

Memory

19.8MiB live, 19.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log1p.f64 x)
(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)
x

Outputs
(log1p.f64 x)
(fma.f64 (fma.f64 x #s(literal 1/3 binary64) #s(literal -1/2 binary64)) (*.f64 x x) x)
x

soundness766.0ms (19.6%)

Memory

16.2MiB live, 287.9MiB allocated

Rules

17 822×	`accelerator-lowering-fma.f32`
17 822×	`accelerator-lowering-fma.f64`
6 606×	`accelerator-lowering-fma.f32`
6 606×	`accelerator-lowering-fma.f64`
4 022×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
1	20	7
2	129	7
3	980	7
0	8596	5
0	62	169
1	171	155
2	363	150
3	980	148
4	2419	144
5	4413	144
6	5329	144
7	6636	144
8	7416	144
9	7564	144
10	7608	144
11	7610	144
12	7610	144
13	7853	144
14	7970	144
15	7978	144
16	7986	144
17	7986	144
0	8425	138

Stop Event

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

Compiler

Compiled 28 to 16 computations (42.9% saved)

preprocess69.0ms (1.8%)

Memory: -41.4MiB live, 137.4MiB allocated
Compiler: Compiled 76 to 40 computations (47.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

sample355.0ms (9.1%)

preprocess16.0ms (0.4%)

explain48.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize14.0ms (0.4%)

series2.0ms (0%)

rewrite338.0ms (8.6%)

simplify978.0ms (25%)

eval84.0ms (2.1%)

prune66.0ms (1.7%)

simplify28.0ms (0.7%)

localize66.0ms (1.7%)

series13.0ms (0.3%)

rewrite441.0ms (11.3%)

simplify433.0ms (11%)

eval63.0ms (1.6%)

prune80.0ms (2%)

regimes33.0ms (0.8%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

simplify7.0ms (0.2%)

soundness766.0ms (19.6%)

preprocess69.0ms (1.8%)

end0.0ms (0%)

Profiling