Metrics for Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

1.1MiB live, 1.1MiB 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
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample1.7s (28.4%)

Memory

-15.9MiB live, 576.2MiB allocated

Samples

1.1s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 169.0ms

ival-div: 91.0ms (54% of total)

ival-sub: 64.0ms (38% of total)

ival-true: 6.0ms (3.6% of total)

exact: 5.0ms (3% of total)

ival-assert: 3.0ms (1.8% of total)

Bogosity

explain169.0ms (2.9%)

Memory

4.2MiB live, 120.1MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`
-	-	`(-.f64 #s(literal 1 binary64) x)`
-	-	`#s(literal 1 binary64)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

126.0ms

512×

valid

Compiler

Compiled 59 to 34 computations (42.4% saved)

Precisions

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

ival-div: 4.0ms (50.1% of total)

ival-sub: 3.0ms (37.6% of total)

ival-true: 1.0ms (12.5% of total)

exact: 0.0ms (0% of total)

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

preprocess24.0ms (0.4%)

Memory

10.4MiB live, 51.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 5 to 4 computations (20% saved)

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Compiler

Compiled 5 to 4 computations (20% saved)

simplify5.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB 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	0	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
x
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)

localize15.0ms (0.2%)

Memory

-5.2MiB live, 34.3MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.00390625	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Samples

9.0ms

256×

valid

Compiler

Compiled 22 to 10 computations (54.5% saved)

Precisions

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

ival-div: 3.0ms (66.8% of total)

ival-sub: 1.0ms (22.3% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

3.5MiB live, 3.5MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.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 (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.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 (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.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 (* -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 (* -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 (* -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 (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -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 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* x (- (/ 1 x) 1)) (taylor inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt (/.f64 x (-.f64 #s(literal 1 binary64) x)) (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (-.f64 #s(literal 1 binary64) x) (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* 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 (* -1 (* 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 (* -1 (* 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	((/ x (- 1 x)) (- 1 x))
0.0ms	x	@	inf	((/ x (- 1 x)) (- 1 x))
0.0ms	x	@	0	((/ x (- 1 x)) (- 1 x))

simplify284.0ms (4.8%)

Memory

-18.9MiB live, 139.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	135
1	93	120
2	220	114
3	545	112
4	1047	112
5	1955	112
6	3384	112
7	4540	112
8	4656	112
9	4656	112
10	4818	112
11	4893	112
12	4893	112
0	4893	109

Stop Event

1×	iter limit
1×	saturated

Counts

24 → 23

Calls

Call 1

Inputs
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))

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

rewrite148.0ms (2.5%)

Memory

8.3MiB live, 148.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	8
0	6	8
1	29	8
2	183	8
3	1612	8
0	9347	8

Stop Event

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

Counts

2 → 425

Calls

Call 1

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

Outputs
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eval75.0ms (1.3%)

Memory: 4.5MiB live, 75.6MiB allocated
Compiler: Compiled 10 226 to 1 289 computations (87.4% saved)

prune11.0ms (0.2%)

Memory

-10.2MiB live, 26.6MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	444	4	448
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	444	5	449

Accuracy

100.0%

Counts

449 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.9%	(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	45.4%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
▶	44.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	56.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify184.0ms (3.1%)

Memory

18.7MiB live, 227.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x x)
cost-diff	0	(neg.f64 (fma.f64 x x x))
cost-diff	128	(+.f64 #s(literal -1 binary64) (*.f64 x x))
cost-diff	704	(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
cost-diff	0	(fma.f64 x x x)
cost-diff	0	(fma.f64 (fma.f64 x x x) x x)
cost-diff	0	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
cost-diff	0	(fma.f64 x x x)
cost-diff	0	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
cost-diff	0	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
0	21	78
1	39	78
2	86	78
3	213	72
4	502	72
5	1703	72
6	5964	72
0	8043	71

Stop Event

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

Calls

Call 1

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

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

localize35.0ms (0.6%)

Memory

-8.7MiB live, 65.4MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(+.f64 #s(literal -1 binary64) (*.f64 x x))
accuracy	0	(*.f64 x x)
accuracy	0	(neg.f64 (fma.f64 x x x))
accuracy	17.88697878092816	(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
accuracy	0	(fma.f64 x x x)
accuracy	0.0234375	(fma.f64 (fma.f64 x x x) x x)
accuracy	34.94593551052783	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
accuracy	0	(fma.f64 x x x)
accuracy	35.668347190153305	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
accuracy	27.659873861959152	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Samples

24.0ms

256×

valid

Compiler

Compiled 135 to 25 computations (81.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-div: 3.0ms (22.6% of total)

ival-add: 3.0ms (22.6% of total)

ival-mult: 3.0ms (22.6% of total)

ival-sub: 2.0ms (15% of total)

ival-neg: 1.0ms (7.5% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

9 → 108

Calls

Call 1

Inputs
#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())
#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())
#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())
#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())
#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())
#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())
#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x 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 (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt x (taylor 0 x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 x)) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 x)))) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* x (+ 1 (* x (+ 1 (* x (+ 1 x)))))) (taylor 0 x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt -1 (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 1) (taylor 0 x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor 0 x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -1 x) 1)) (taylor 0 x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -1 x) 1)) (taylor 0 x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* x (- (* -1 x) 1)) (taylor 0 x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1 (+ (/ 1 x) (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x))) (taylor inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x 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 (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (patch #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 x x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 x x x) (patch (fma.f64 x x x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) (patch #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 3) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* (pow x 3) (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 3) (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1))) (taylor -inf x) (#s(alt (fma.f64 (fma.f64 x x x) x x) (patch (fma.f64 (fma.f64 x x x) x x) #<representation binary64>) () ())) ())
#s(alt -1 (taylor -inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (* -1 (+ 1 (/ 1 x))) (taylor -inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (/ 1 x)) x)) 1) (taylor -inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1) (taylor -inf x) (#s(alt (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) (patch (/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (.f64 x x))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (/ 1 (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 #s(literal -1 binary64) (.f64 x x)) (patch (+.f64 #s(literal -1 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (pow x 2)) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x x x)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* (pow x 2) (+ 1 (/ 1 x)))) (taylor -inf x) (#s(alt (neg.f64 (fma.f64 x x x)) (patch (neg.f64 (fma.f64 x 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 (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	x	@	inf	((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (neg (+ (* x x) x)) (+ -1 (* x x))) (+ -1 (* x x)) (neg (+ (* x x) x)) (* x x))
1.0ms	x	@	-inf	((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (neg (+ (* x x) x)) (+ -1 (* x x))) (+ -1 (* x x)) (neg (+ (* x x) x)) (* x x))
1.0ms	x	@	0	((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (neg (+ (* x x) x)) (+ -1 (* x x))) (+ -1 (* x x)) (neg (+ (* x x) x)) (* x x))

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify191.0ms (3.2%)

Memory

-13.7MiB live, 107.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	664
1	129	640
2	366	603
3	1145	595
4	2989	595
5	6208	595
0	8133	542

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 102

Calls

Call 1

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

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

rewrite183.0ms (3.1%)

Memory

-9.7MiB live, 191.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
0	21	65
1	96	59
2	702	59
0	8334	58

Stop Event

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

Counts

9 → 793

Calls

Call 1

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

Outputs
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eval179.0ms (3%)

Memory: 30.0MiB live, 215.0MiB allocated
Compiler: Compiled 23 710 to 2 660 computations (88.8% saved)

prune40.0ms (0.7%)

Memory

-20.8MiB live, 64.0MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	1 216	3	1 219
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	1 217	7	1 224

Accuracy

100.0%

Counts

1 224 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	71.9%	(/.f64 (fma.f64 x x x) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	45.4%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	44.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	44.3%	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 #s(literal 1 binary64) x) x))
▶	2.9%	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
✓	56.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 41 to 29 computations (29.3% saved)

simplify184.0ms (3.1%)

Memory

11.2MiB live, 203.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(neg.f64 x)
cost-diff	0	(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
cost-diff	0	(fma.f64 x x x)
cost-diff	704	(/.f64 (fma.f64 x x x) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
cost-diff	0	(+.f64 #s(literal 1 binary64) x)
cost-diff	0	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 #s(literal 1 binary64) x) x))
cost-diff	128	(*.f64 (+.f64 #s(literal 1 binary64) x) x)
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) x) (*.f64 x x))
cost-diff	0	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	16	70
0	24	68
1	38	68
2	56	68
3	71	68
4	126	68
5	204	68
6	533	63
7	1966	63
8	3859	63
9	6005	63
10	7046	63
11	7768	63
0	8076	63

Stop Event

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

Calls

Call 1

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

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

localize69.0ms (1.2%)

Memory

-1.1MiB live, 98.8MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 (neg.f64 x) x #s(literal 1 binary64))
accuracy	0	(fma.f64 x x x)
accuracy	0	(neg.f64 x)
accuracy	17.88697878092816	(/.f64 (fma.f64 x x x) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
accuracy	0	(+.f64 #s(literal 1 binary64) x)
accuracy	0.015625	(*.f64 (+.f64 #s(literal 1 binary64) x) x)
accuracy	35.668347190153305	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 #s(literal 1 binary64) x) x))
accuracy	0	(*.f64 x x)
accuracy	27.167981222220657	#s(approx (+ (* x x) x) (*.f64 x x))
accuracy	35.668347190153305	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))

Samples

24.0ms

256×

valid

Compiler

Compiled 110 to 26 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 5.0ms (33.5% of total)

ival-div: 3.0ms (20.1% of total)

ival-add: 3.0ms (20.1% of total)

ival-sub: 2.0ms (13.4% of total)

ival-neg: 1.0ms (6.7% of total)

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

exact: 0.0ms (0% of total)

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

series22.0ms (0.4%)

Memory

-32.5MiB live, 6.2MiB allocated

Counts

10 → 120

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify505.0ms (8.5%)

Memory

37.1MiB live, 188.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	591
1	101	564
2	215	546
3	704	540
4	2823	540
5	4988	540
0	8231	498

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 112

Calls

Call 1

Inputs
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
1
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(+ 1 (* -1 (pow x 2)))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* (pow x 2) (- (/ 1 (pow x 2)) 1))
(* -1 x)
(* -1 x)
(* -1 x)
(* -1 x)

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

rewrite148.0ms (2.5%)

Memory

0.9MiB live, 234.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	65
0	24	63
1	89	58
2	619	58
0	9155	57

Stop Event

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

Counts

10 → 1 057

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval193.0ms (3.3%)

Memory: -0.4MiB live, 277.7MiB allocated
Compiler: Compiled 20 730 to 2 525 computations (87.8% saved)

prune29.0ms (0.5%)

Memory

-23.3MiB live, 63.3MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	1 168	1	1 169
Fresh	0	0	0
Picked	1	2	3
Done	0	4	4
Total	1 169	7	1 176

Accuracy

100.0%

Counts

1 176 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.9%	(/.f64 (fma.f64 x x x) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	45.4%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	44.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
✓	44.3%	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 #s(literal 1 binary64) x) x))
▶	45.0%	#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x))
✓	56.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 41 to 30 computations (26.8% saved)

simplify5.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (+ 1 x) #s(literal 1 binary64))
cost-diff	0	(*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)
cost-diff	0	#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x))
(*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)
#s(approx (+ 1 x) #s(literal 1 binary64))
#s(literal 1 binary64)
x

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

localize18.0ms (0.3%)

Memory

27.3MiB live, 27.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.015625	(*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)
accuracy	35.298173808642815	#s(approx (+ 1 x) #s(literal 1 binary64))
accuracy	35.668347190153305	#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x))

Samples

12.0ms

256×

valid

Compiler

Compiled 30 to 13 computations (56.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-sub: 2.0ms (28.9% of total)

ival-div: 2.0ms (28.9% of total)

ival-mult: 2.0ms (28.9% of total)

ival-add: 1.0ms (14.5% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

-31.7MiB live, 4.9MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

#s(alt #s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)) (patch #s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)) #<representation binary64>) () ())

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

#s(alt #s(approx (+ 1 x) #s(literal 1 binary64)) (patch #s(approx (+ 1 x) #s(literal 1 binary64)) #<representation binary64>) () ())

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

Calls

3 calls:

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

simplify197.0ms (3.3%)

Memory

32.6MiB live, 224.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	176
1	89	170
2	197	164
3	620	162
4	2726	162
5	5294	162
0	8123	148

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 32

Calls

Call 1

Inputs
x
(* x (+ 1 x))
(* x (+ 1 (* x (+ 1 x))))
(* x (+ 1 (* x (+ 1 (* x (+ 1 x))))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
-1
(* -1 (+ 1 (/ 1 x)))
(- (* -1 (/ (+ 1 (/ 1 x)) x)) 1)
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))

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

rewrite135.0ms (2.3%)

Memory

6.8MiB live, 129.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	25
0	9	25
1	38	25
2	244	25
3	2471	25
0	11451	25

Stop Event

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

Counts

3 → 8

Calls

Call 1

Inputs
#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x))
(*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)
#s(approx (+ 1 x) #s(literal 1 binary64))

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>

eval7.0ms (0.1%)

Memory: -29.3MiB live, 8.6MiB allocated
Compiler: Compiled 265 to 49 computations (81.5% saved)

prune5.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	40	7	47

Accuracy

100.0%

Counts

47 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	71.9%	(/.f64 (fma.f64 x x x) (fma.f64 (neg.f64 x) x #s(literal 1 binary64)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	45.4%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	44.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
✓	44.3%	#s(approx (/ x (- 1 x)) (*.f64 (+.f64 #s(literal 1 binary64) x) x))
✓	45.0%	#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x))
✓	56.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 98 to 55 computations (43.9% saved)

regimes7.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB allocated

Counts

9 → 1

Calls

Call 1

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

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))

Calls

2 calls:

3.0ms	x
3.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes5.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Counts

6 → 2

Calls

Call 1

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

Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))

Calls

2 calls:

3.0ms	x
2.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
99.2%	3	`x`
99.2%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes5.0ms (0.1%)

Memory

-30.8MiB live, 5.8MiB allocated

Counts

5 → 2

Calls

Call 1

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

Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) (fma.f64 x x x))

Calls

1 calls:

4.0ms

(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
98.9%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes2.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x))

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

Calls

1 calls:

2.0ms

(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
98.3%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Accuracy

Total -35.3b remaining (-127.5%)

Threshold costs -35.3b (-127.5%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))

Outputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Calls

2 calls:

1.0ms	x
1.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
56.8%	1	`x`
56.8%	1	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999061662819801	-0.005314990941554031

Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999061662819801	-0.005314990941554031

Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999061662819801	-0.005314990941554031

Compiler

Compiled 8 to 8 computations (0% saved)

simplify67.0ms (1.1%)

Memory

-21.9MiB live, 79.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	93
1	27	93
2	30	93
3	32	93
4	33	93

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Outputs
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (fma.f64 x x x)))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) (*.f64 #s(approx (+ 1 x) #s(literal 1 binary64)) x)))
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

soundness1.0s (17.5%)

Memory

11.7MiB live, 434.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
0	21	65
1	96	59
2	702	59
0	8334	58
0	33	591
1	101	564
2	215	546
3	704	540
4	2823	540
5	4988	540
0	8231	498
0	33	135
1	93	120
2	220	114
3	545	112
4	1047	112
5	1955	112
6	3384	112
7	4540	112
8	4656	112
9	4656	112
10	4818	112
11	4893	112
12	4893	112
0	4893	109

Stop Event

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

Compiler

Compiled 83 to 40 computations (51.8% saved)

preprocess36.0ms (0.6%)

Memory: -3.1MiB live, 70.7MiB allocated
Compiler: Compiled 120 to 44 computations (63.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27

start0.0ms (0%)

analyze1.0ms (0%)

sample1.7s (28.4%)

explain169.0ms (2.9%)

preprocess24.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize15.0ms (0.2%)

series1.0ms (0%)

simplify284.0ms (4.8%)

rewrite148.0ms (2.5%)

eval75.0ms (1.3%)

prune11.0ms (0.2%)

simplify184.0ms (3.1%)

localize35.0ms (0.6%)

series5.0ms (0.1%)

simplify191.0ms (3.2%)

rewrite183.0ms (3.1%)

eval179.0ms (3%)

prune40.0ms (0.7%)

simplify184.0ms (3.1%)

localize69.0ms (1.2%)

series22.0ms (0.4%)

simplify505.0ms (8.5%)

rewrite148.0ms (2.5%)

eval193.0ms (3.3%)

prune29.0ms (0.5%)

simplify5.0ms (0.1%)

localize18.0ms (0.3%)

series6.0ms (0.1%)

simplify197.0ms (3.3%)

rewrite135.0ms (2.3%)

eval7.0ms (0.1%)

prune5.0ms (0.1%)

regimes7.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes3.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify67.0ms (1.1%)

soundness1.0s (17.5%)

preprocess36.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	15
1	20	11
2	47	10
3	100	10
4	195	10
5	284	10
6	295	10
7	309	10
8	322	10
0	4	5
0	6	5
1	10	5
2	14	5
3	19	5
4	26	5
5	36	5
6	51	5
7	74	5
8	96	5
9	104	5
10	106	5
0	106	5

Iter	Nodes	Cost
0	4	10
0	6	10
1	10	10
2	14	10
3	19	10
4	26	10
5	36	10
6	51	10
7	74	10
8	96	10
9	104	10
10	106	10
0	106	10

Iter	Nodes	Cost
0	8	27
0	9	27
1	15	27
2	19	27
3	24	27
4	31	27
5	41	27
6	56	27
7	86	27
8	111	27
9	119	27
10	121	27
0	121	27