Metrics for ln(1 + x)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

1.8MiB live, 1.8MiB 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)

sample476.0ms (10.3%)

Memory

15.2MiB live, 470.2MiB allocated

Samples

311.0ms	8 256×	0	valid
0.0ms	1×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 82.0ms

ival-log1p: 74.0ms (90.4% of total)

ival-true: 5.0ms (6.1% of total)

ival-assert: 3.0ms (3.7% of total)

Bogosity

explain305.0ms (6.6%)

Memory

-15.0MiB live, 68.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
168	-	1	(0.01881398191421487)	`(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	167	1

Confusion

	Predicted +	Predicted -
+	167	1
-	0	88

Precision

1.0

Recall

0.9940476190476191

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	167	1	0
-	0	0	88

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	89
1	167

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 26 to 16 computations (38.5% saved)

Precisions

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

ival-log1p: 5.0ms (60.5% of total)

ival-add: 3.0ms (36.3% of total)

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

exact: 0.0ms (0% of total)

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

preprocess13.0ms (0.3%)

Memory

21.2MiB live, 21.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	15	9
2	22	9
3	30	9
4	40	9
5	53	9
6	66	9
7	69	9
0	4	4
0	6	4
1	9	4
0	9	2

Stop Event

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

Calls

Call 1

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

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

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.0%	(log.f64 (+.f64 #s(literal 1 binary64) x))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify3.0ms (0.1%)

Memory

4.7MiB live, 4.7MiB 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×	`lower-+.f32`
2×	`lower-log1p.f32`
2×	`lift-+.f64`
2×	`lower-+.f64`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	9	9
0	9	7

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.4%)

Memory

-15.7MiB live, 20.7MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	38.381577705964936	(log.f64 (+.f64 #s(literal 1 binary64) x))

Samples

15.0ms

256×

valid

Compiler

Compiled 11 to 6 computations (45.5% saved)

Precisions

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

ival-add: 8.0ms (72.2% of total)

ival-log1p: 3.0ms (27.1% 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

2.8MiB live, 2.8MiB allocated

Counts

2 → 24

Calls

Call 1

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

Inputs

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

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

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

Calls

3 calls:

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

simplify253.0ms (5.5%)

Memory

6.5MiB live, 163.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 648×	`lower-fma.f64`
12 648×	`lower-fma.f32`
2 520×	`lower-*.f64`
2 520×	`lower-*.f32`
2 072×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	169
1	171	155
2	363	150
3	979	148
4	2422	144
5	4452	144
6	5392	144
7	6689	144
8	7472	144
9	7620	144
10	7664	144
11	7666	144
12	7666	144
13	7909	144
0	8006	138

Stop Event

1×	iter limit
1×	node limit

Counts

24 → 21

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
(+ 1 x)
(+ 1 x)
(+ 1 x)
(* -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)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(+ (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 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))

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

rewrite279.0ms (6%)

Memory

10.7MiB live, 251.0MiB allocated

Rules

6 606×	`lower-fma.f64`
6 606×	`lower-fma.f32`
4 022×	`lower-/.f64`
4 022×	`lower-/.f32`
3 648×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	22	7
2	131	7
3	984	7
0	8620	5

Stop Event

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

Counts

2 → 344

Calls

Call 1

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

Outputs
(.f64 (.f64 (+.f64 (log1p.f64 (.f64 (neg.f64 x) x)) (log1p.f64 (neg.f64 x))) (log1p.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (log1p.f64 (.f64 (neg.f64 x) x)) (log1p.f64 (neg.f64 x)))))
(.f64 (.f64 (+.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64))) (log1p.f64 (-.f64 (.f64 x x) x))) (log1p.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64))) (log1p.f64 (-.f64 (.f64 x x) x)))))
(.f64 (-.f64 (pow.f64 (log1p.f64 (.f64 (neg.f64 x) x)) #s(literal 3 binary64)) (pow.f64 (log1p.f64 (neg.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log1p.f64 (.f64 (neg.f64 x) x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (log1p.f64 (neg.f64 x)) #s(literal 2 binary64)) (.f64 (log1p.f64 (*.f64 (neg.f64 x) x)) (log1p.f64 (neg.f64 x)))))))
(.f64 (-.f64 (pow.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (log1p.f64 (-.f64 (.f64 x x) x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (+.f64 (pow.f64 (log1p.f64 (-.f64 (.f64 x x) x)) #s(literal 2 binary64)) (.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64))) (log1p.f64 (-.f64 (*.f64 x x) x)))))))
(*.f64 #s(literal -1 binary64) (neg.f64 (log1p.f64 x)))
(log1p.f64 x)
(/.f64 (-.f64 (.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) (log.f64 (fma.f64 x x #s(literal -1 binary64)))) (.f64 (log.f64 (-.f64 x #s(literal 1 binary64))) (log.f64 (-.f64 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 (-.f64 (.f64 (log.f64 (-.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (-.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64))))) (.f64 (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64))))) (+.f64 (log.f64 (-.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3 binary64)))) (log.f64 (fma.f64 (-.f64 #s(literal 1 binary64) x) x #s(literal -1 binary64)))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 (neg.f64 (log1p.f64 x)) (neg.f64 (log1p.f64 x)))) (+.f64 #s(literal 0 binary64) (neg.f64 (log1p.f64 x))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (.f64 (neg.f64 x) x)) #s(literal 2 binary64)) (.f64 (neg.f64 (log1p.f64 (neg.f64 x))) (neg.f64 (log1p.f64 (neg.f64 x))))) (-.f64 (log1p.f64 (*.f64 (neg.f64 x) x)) (neg.f64 (log1p.f64 (neg.f64 x)))))
(/.f64 (-.f64 (pow.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (.f64 (neg.f64 (log1p.f64 (-.f64 (.f64 x x) x))) (neg.f64 (log1p.f64 (-.f64 (.f64 x x) x))))) (-.f64 (log1p.f64 (pow.f64 x #s(literal 3 binary64))) (neg.f64 (log1p.f64 (-.f64 (.f64 x x) x)))))
(/.f64 (-.f64 (pow.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 (-.f64 x #s(literal 1 binary64))) #s(literal 3 binary64))) (fma.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) (log.f64 (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (log.f64 (-.f64 x #s(literal 1 binary64))) (log.f64 (-.f64 x #s(literal 1 binary64))) (*.f64 (log.f64 (fma.f64 x x #s(literal -1 binary64))) (log.f64 (-.f64 x #s(literal 1 binary64)))))))
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eval54.0ms (1.2%)

Memory: -11.0MiB live, 95.8MiB allocated
Compiler: Compiled 9 051 to 1 130 computations (87.5% saved)

prune6.0ms (0.1%)

Memory

24.2MiB live, 24.2MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	361	4	365
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	362	4	366

Accuracy

100.0%

Counts

366 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(log1p.f64 x)
▶	65.8%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
▶	66.7%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
▶	65.6%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

Compiler

Compiled 32 to 26 computations (18.8% saved)

simplify22.0ms (0.5%)

Memory

-27.9MiB live, 20.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(log1p.f64 x)
cost-diff	0	(fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
cost-diff	0	(fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
cost-diff	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
cost-diff	0	(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

Rules

1 072×	`lower-fma.f32`
1 060×	`lower-fma.f64`
340×	`lower-*.f32`
334×	`lower-*.f64`
286×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	114
0	35	114
1	53	114
2	91	114
3	198	114
4	427	114
5	691	114
6	754	114
0	754	114

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize60.0ms (1.3%)

Memory

0.3MiB live, 111.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(log1p.f64 x)
accuracy	0.00390625	(fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64))
accuracy	0.03125	(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.0390625	(fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy	21.90449166715322	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
accuracy	0.03515625	(fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))
accuracy	0.046875	(*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x)
accuracy	0.1328125	(fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64))
accuracy	21.291273087136055	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
accuracy	0	(fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))
accuracy	0.015625	(*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x)
accuracy	22.036190217321813	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))

Samples

38.0ms

256×

valid

Compiler

Compiled 110 to 23 computations (79.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 13.0ms (48.8% of total)

ival-add: 7.0ms (26.3% of total)

const: 4.0ms (15% of total)

ival-log1p: 3.0ms (11.3% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.2%)

Memory

25.7MiB live, 25.7MiB allocated

Counts

13 → 156

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

inf

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

2.0ms

-inf

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

1.0ms

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

simplify398.0ms (8.6%)

Memory

8.9MiB live, 166.6MiB allocated

Algorithm

1×	egg-herbie

Rules

14 010×	`lower-fma.f64`
14 010×	`lower-fma.f32`
2 926×	`lower-*.f64`
2 926×	`lower-*.f32`
2 714×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	135	1310
1	385	1238
2	1179	1214
3	4066	1182
4	7899	1182
0	8300	1053

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 149

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

rewrite539.0ms (11.6%)

Memory

-15.5MiB live, 271.2MiB allocated

Rules

7 758×	`lower-fma.f32`
7 746×	`lower-fma.f64`
4 884×	`lower-*.f32`
4 878×	`lower-*.f64`
3 964×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	101
0	35	101
1	134	101
2	982	101
0	8466	101

Stop Event

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

Counts

13 → 455

Calls

Call 1

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

Outputs
#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
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(fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64))
(fma.f64 x #s(literal -1/4 binary64) #s(literal 1/3 binary64))
(-.f64 (/.f64 #s(literal 1/9 binary64) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/4 binary64) x))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (-.f64 #s(literal 1/3 binary64) (.f64 #s(literal -1/4 binary64) x))))
(-.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (fma.f64 #s(literal -1/4 binary64) x #s(literal -1/3 binary64))) (/.f64 #s(literal -1/9 binary64) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1/3 binary64))))
(+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (fma.f64 #s(literal -1/4 binary64) x #s(literal -1/3 binary64))) (neg.f64 (/.f64 #s(literal -1/9 binary64) (fma.f64 #s(literal 1/4 binary64) x #s(literal 1/3 binary64)))))
(+.f64 (*.f64 #s(literal -1/4 binary64) x) #s(literal 1/3 binary64))
(+.f64 #s(literal 1/3 binary64) (*.f64 #s(literal -1/4 binary64) x))

eval87.0ms (1.9%)

Memory: 17.1MiB live, 208.4MiB allocated
Compiler: Compiled 12 940 to 2 221 computations (82.8% saved)

prune19.0ms (0.4%)

Memory

-14.3MiB live, 64.4MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	601	3	604
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	601	7	608

Accuracy

100.0%

Counts

608 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)
▶	65.6%	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
✓	65.8%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
✓	66.7%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
▶	65.8%	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))) x))
✓	65.6%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
▶	66.2%	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 59 to 47 computations (20.3% saved)

simplify19.0ms (0.4%)

Memory

15.0MiB live, 51.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
cost-diff	0	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
cost-diff	0	(fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))
cost-diff	0	(.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))) x)
cost-diff	0	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))) x))
cost-diff	320	(fma.f64 x #s(literal -1/2 binary64) (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64)))
cost-diff	0	#s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64))
cost-diff	0	(.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))

Rules

1 072×	`lower-fma.f32`
1 064×	`lower-fma.f64`
352×	`lower-*.f32`
346×	`lower-*.f64`
232×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	141
0	34	141
1	62	141
2	124	141
3	249	141
4	543	141
5	703	141
6	703	141
0	703	123

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize275.0ms (5.9%)

Memory

-21.2MiB live, 140.9MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x)
accuracy	22.036190217321813	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
accuracy	0.01171875	(fma.f64 x #s(literal -1/2 binary64) (fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64)))
accuracy	0.03125	(.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))) x)
accuracy	0.04296875	(fma.f64 (*.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))
accuracy	21.90449166715322	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))) x))
accuracy	0.03125	(.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)
accuracy	21.90449166715322	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))
accuracy	22.60040421988763	#s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64))

Samples

260.0ms

256×

valid

Compiler

Compiled 112 to 23 computations (79.5% saved)

Precisions

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

ival-mult: 35.0ms (72.9% of total)

ival-add: 7.0ms (14.6% of total)

ival-log1p: 3.0ms (6.3% of total)

const: 3.0ms (6.3% of total)

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

exact: 0.0ms (0% of total)

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

series7.0ms (0.2%)

Memory

12.7MiB live, 12.7MiB allocated

Counts

10 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify206.0ms (4.4%)

Memory

-0.7MiB live, 183.9MiB allocated

Algorithm

1×	egg-herbie

Rules

9 748×	`lower-fma.f64`
9 748×	`lower-fma.f32`
3 126×	`lower-*.f64`
3 126×	`lower-*.f32`
2 078×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	121	1153
1	352	1076
2	1047	1064
3	3438	1022
4	7745	1022
0	8191	940

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 114

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

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

rewrite376.0ms (8.1%)

Memory

15.8MiB live, 258.2MiB allocated

Rules

9 104×	`lower-fma.f32`
9 096×	`lower-fma.f64`
4 132×	`lower-*.f32`
4 126×	`lower-*.f64`
3 526×	`lower-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	125
0	34	125
1	146	125
2	1149	125
0	8299	107

Stop Event

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

Counts

10 → 384

Calls

Call 1

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

Outputs
#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))
(.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x)
(.f64 x #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)))
#s(approx (+ (* (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (*.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x))))
(.f64 (-.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/4 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) (.f64 #s(literal -1/2 binary64) x))))
(.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) x (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)))))
(.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (hypot.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)))))))
(.f64 (neg.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(.f64 (neg.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x)) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64))))))
(.f64 (-.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64))) (pow.f64 (fma.f64 x (-.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64))))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 3 binary64))) (pow.f64 (-.f64 (hypot.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) x) (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (*.f64 x x) #s(literal 1 binary64)))) #s(literal -1 binary64)))
(.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64))))))
(.f64 (+.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 (+.f64 (-.f64 #s(literal 1 binary64) (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x)) (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64))) (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64)))) (.f64 (/.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64))) (/.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64))))) (+.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (.f64 x x)) (fma.f64 x (-.f64 #s(literal -1/2 binary64) (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64))) (/.f64 (pow.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x) #s(literal 1 binary64)) #s(literal 2 binary64)) (fma.f64 x (-.f64 #s(literal -1/2 binary64) (*.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x)) #s(literal -1 binary64)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64))) (/.f64 (pow.f64 (.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64)))) (.f64 (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (*.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x) #s(literal 2 binary64)) (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64))) (pow.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64))) (.f64 (pow.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) (.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) (.f64 x x))))
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(*.f64 x x)
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eval150.0ms (3.2%)

Memory: -21.9MiB live, 119.7MiB allocated
Compiler: Compiled 12 343 to 1 703 computations (86.2% saved)

prune26.0ms (0.6%)

Memory

11.7MiB live, 49.7MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	518	0	518
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	518	7	525

Accuracy

100.0%

Counts

525 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(log1p.f64 x)
✓	65.6%	#s(approx (log (+ 1 x)) (fma.f64 (*.f64 x x) #s(literal -1/2 binary64) x))
✓	65.8%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
✓	66.7%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 (fma.f64 #s(literal 1/3 binary64) x #s(literal -1/2 binary64)) x #s(literal 1 binary64)) x))
✓	65.8%	#s(approx (log (+ 1 x)) (.f64 (fma.f64 x #s(literal -1/2 binary64) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/4 binary64) x #s(literal 1/3 binary64)) #s(literal 1 binary64))) x))
✓	65.6%	#s(approx (log (+ 1 x)) (*.f64 (fma.f64 #s(literal -1/2 binary64) x #s(literal 1 binary64)) x))
✓	66.2%	#s(approx (log (+ 1 x)) (.f64 #s(approx (+ ( (+ (* (+ (* -1/4 x) 1/3) x) -1/2) x) 1) #s(literal 1 binary64)) x))

Compiler

Compiled 122 to 77 computations (36.9% saved)

regimes10.0ms (0.2%)

Memory

-12.9MiB live, 25.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(log1p.f64 x)

Calls

3 calls:

4.0ms	(+.f64 #s(literal 1 binary64) x)
3.0ms	x
2.0ms	(log.f64 (+.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 8 to 8 computations (0% saved)

regimes9.0ms (0.2%)

Memory

-14.2MiB live, 24.0MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

3 calls:

4.0ms	x
2.0ms	(+.f64 #s(literal 1 binary64) x)
2.0ms	(log.f64 (+.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
66.7%	1	`x`
66.7%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
66.7%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 8 to 8 computations (0% saved)

regimes5.0ms (0.1%)

Memory

17.9MiB live, 17.9MiB allocated

Accuracy

Total -1.0b remaining (-4.6%)

Threshold costs -1b (-4.6%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

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

Results

Accuracy	Segments	Branch
66.2%	1	`x`
66.2%	1	`(log.f64 (+.f64 #s(literal 1 binary64) x))`
66.2%	1	`(+.f64 #s(literal 1 binary64) x)`

Compiler

Compiled 8 to 8 computations (0% saved)

simplify30.0ms (0.6%)

Memory

12.6MiB live, 94.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`
2×	`1-exp-binary32-exp.f32`
2×	`1-exp-binary64-exp.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	26	38

Stop Event

1×

saturated

Calls

Call 1

Inputs

(log1p.f64 x)

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

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

Outputs

(log1p.f64 x)

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

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

soundness927.0ms (20%)

Memory

8.0MiB live, 434.3MiB allocated

Rules

14 010×	`lower-fma.f64`
14 010×	`lower-fma.f32`
12 648×	`lower-fma.f64`
12 648×	`lower-fma.f32`
6 606×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	22	7
2	131	7
3	984	7
0	8620	5
0	135	1310
1	385	1238
2	1179	1214
3	4066	1182
4	7899	1182
0	8300	1053
0	62	169
1	171	155
2	363	150
3	979	148
4	2422	144
5	4452	144
6	5392	144
7	6689	144
8	7472	144
9	7620	144
10	7664	144
11	7666	144
12	7666	144
13	7909	144
0	8006	138

Stop Event

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

Compiler

Compiled 48 to 37 computations (22.9% saved)

preprocess45.0ms (1%)

Memory: 11.0MiB live, 117.6MiB allocated
Compiler: Compiled 80 to 50 computations (37.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	24	141
0	34	141
1	62	141
2	124	141
3	249	141
4	543	141
5	703	141
6	703	141
0	703	123

Iter	Nodes	Cost
0	24	141
0	34	141
1	62	141
2	124	141
3	249	141
4	543	141
5	703	141
6	703	141
0	703	123

start0.0ms (0%)

analyze1.0ms (0%)

sample476.0ms (10.3%)

explain305.0ms (6.6%)

preprocess13.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize20.0ms (0.4%)

series2.0ms (0%)

simplify253.0ms (5.5%)

rewrite279.0ms (6%)

eval54.0ms (1.2%)

prune6.0ms (0.1%)

simplify22.0ms (0.5%)

localize60.0ms (1.3%)

series10.0ms (0.2%)

simplify398.0ms (8.6%)

rewrite539.0ms (11.6%)

eval87.0ms (1.9%)

prune19.0ms (0.4%)

simplify19.0ms (0.4%)

localize275.0ms (5.9%)

series7.0ms (0.2%)

simplify206.0ms (4.4%)

rewrite376.0ms (8.1%)

eval150.0ms (3.2%)

prune26.0ms (0.6%)

regimes10.0ms (0.2%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

simplify30.0ms (0.6%)

soundness927.0ms (20%)

preprocess45.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	24	141
0	34	141
1	62	141
2	124	141
3	249	141
4	543	141
5	703	141
6	703	141
0	703	123