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

2.3MiB live, 2.3MiB 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)

sample683.0ms (10.9%)

Memory

-26.0MiB live, 851.6MiB allocated

Samples

435.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 166.0ms

ival-div: 79.0ms (47.7% of total)

ival-sub: 68.0ms (41% of total)

ival-assert: 7.0ms (4.2% of total)

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

exact: 5.0ms (3% of total)

Bogosity

explain58.0ms (0.9%)

Memory

32.9MiB live, 70.0MiB 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

17.0ms

512×

valid

Compiler

Compiled 29 to 16 computations (44.8% saved)

Precisions

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

ival-div: 4.0ms (53.3% of total)

ival-sub: 3.0ms (40% of total)

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

exact: 0.0ms (0% of total)

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

preprocess29.0ms (0.5%)

Memory

-15.9MiB live, 27.5MiB 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

1.2MiB live, 1.2MiB 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

8.6MiB live, 8.6MiB 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)

localize16.0ms (0.3%)

Memory

-7.7MiB live, 27.7MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(-.f64 #s(literal 1 binary64) x)
accuracy	0.0078125	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Samples

12.0ms

256×

valid

Compiler

Compiled 12 to 6 computations (50% saved)

Precisions

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

ival-div: 2.0ms (54.6% of total)

ival-sub: 1.0ms (27.3% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.3MiB live, 3.3MiB 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))

simplify149.0ms (2.4%)

Memory

28.8MiB live, 100.1MiB 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)

rewrite169.0ms (2.7%)

Memory

-6.5MiB live, 229.1MiB 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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eval184.0ms (2.9%)

Memory: -17.7MiB live, 93.7MiB allocated
Compiler: Compiled 10 226 to 1 289 computations (87.4% saved)

prune8.0ms (0.1%)

Memory

37.8MiB live, 37.8MiB 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
▶	74.2%	(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	52.3%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
▶	51.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	49.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 40 to 26 computations (35% saved)

simplify424.0ms (6.8%)

Memory

15.1MiB live, 230.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	256	(*.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))
cost-diff	320	(*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x))
cost-diff	512	(*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x))
cost-diff	704	(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) 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	19	110
0	31	96
1	62	90
2	152	82
3	486	82
4	2000	80
5	5435	80
0	8066	79

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 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x)))
(*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x))
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))
(-.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(neg.f64 x)
(*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) 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 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(/.f64 x (-.f64 #s(literal 1 binary64) x))
(-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x)))
(*.f64 (-.f64 #s(literal -1 binary64) x) x)
(*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x))
#s(literal 0 binary64)
#s(literal 0 binary64)
(-.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))
(fma.f64 x x x)
(-.f64 #s(literal -1 binary64) x)
#s(literal -1 binary64)
(neg.f64 x)
(*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(fma.f64 x x #s(literal -1 binary64))

localize98.0ms (1.6%)

Memory

-24.5MiB live, 233.1MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.0078125	(*.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))
accuracy	0.01953125	(*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x))
accuracy	16.396722736684147	(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
accuracy	0	(fma.f64 x x x)
accuracy	0.01171875	(fma.f64 (fma.f64 x x x) x x)
accuracy	30.534744647592746	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
accuracy	0	(fma.f64 x x x)
accuracy	31.14252889481066	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
accuracy	32.128284200974704	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Samples

83.0ms

256×

valid

Compiler

Compiled 101 to 19 computations (81.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-mult: 32.0ms (72.1% of total)

ival-sub: 5.0ms (11.3% of total)

ival-div: 4.0ms (9% of total)

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

ival-neg: 1.0ms (2.3% of total)

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

exact: 0.0ms (0% of total)

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

series10.0ms (0.2%)

Memory

-5.3MiB live, 32.8MiB allocated

Counts

10 → 120

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

Calls

3 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (- (* 0 (- 1 x)) (* (- -1 x) (neg x))) (* (- -1 x) (- 1 x))) (* 0 (- 1 x)) (* (- -1 x) (- 1 x)) (* (- -1 x) (neg x)) (neg x))
1.0ms	x	@	inf	((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (- (* 0 (- 1 x)) (* (- -1 x) (neg x))) (* (- -1 x) (- 1 x))) (* 0 (- 1 x)) (* (- -1 x) (- 1 x)) (* (- -1 x) (neg x)) (neg x))
1.0ms	x	@	0	((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (- (* 0 (- 1 x)) (* (- -1 x) (neg x))) (* (- -1 x) (- 1 x))) (* 0 (- 1 x)) (* (- -1 x) (- 1 x)) (* (- -1 x) (neg x)) (neg x))

Time

Variable

Point

Expression

4.0ms

-inf

((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (- (* 0 (- 1 x)) (* (- -1 x) (neg x))) (* (- -1 x) (- 1 x))) (* 0 (- 1 x)) (* (- -1 x) (- 1 x)) (* (- -1 x) (neg x)) (neg x))

1.0ms

inf

((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (- (* 0 (- 1 x)) (* (- -1 x) (neg x))) (* (- -1 x) (- 1 x))) (* 0 (- 1 x)) (* (- -1 x) (- 1 x)) (* (- -1 x) (neg x)) (neg x))

1.0ms

((/ x (- 1 x)) (/ x (- 1 x)) (+ (* x x) x) (/ x (- 1 x)) (+ (* (+ (* x x) x) x) x) (/ (- (* 0 (- 1 x)) (* (- -1 x) (neg x))) (* (- -1 x) (- 1 x))) (* 0 (- 1 x)) (* (- -1 x) (- 1 x)) (* (- -1 x) (neg x)) (neg x))

simplify169.0ms (2.7%)

Memory

26.7MiB live, 221.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	652
1	118	628
2	323	600
3	1018	592
4	3587	592
5	7193	592
0	8754	538

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 113

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))))))
0
0
0
0
-1
(- (pow x 2) 1)
(- (pow x 2) 1)
(- (pow x 2) 1)
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(* -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)))
-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)))
0
0
0
0
(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))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* -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)
-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)
0
0
0
0
(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))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* -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 (+ 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)))
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 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))
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 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 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #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 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (/ 1 x)) (pow x 2))) (+ 1 (/ 1 x)))
(.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) 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 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) x))
(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 #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 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) x))
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 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))
(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 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 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #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 x #s(literal -1 binary64)) x) x))
(- (* -1 (/ (+ 1 (+ (/ 1 x) (/ 1 (pow x 2)))) x)) 1)
(.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) 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 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) x))
(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 #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 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1 binary64)) (/.f64 (-.f64 x #s(literal -1 binary64)) x))
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 binary64)
0
#s(literal 0 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))
(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 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)
(* -1 x)
(neg.f64 x)

rewrite304.0ms (4.9%)

Memory

11.0MiB live, 197.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	81
0	31	71
1	133	68
2	1003	58
0	9010	57

Stop Event

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

Counts

10 → 1 703

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 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x)))
(*.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(*.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))
(neg.f64 x)

Outputs
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eval551.0ms (8.8%)

Memory: -86.0MiB live, 654.2MiB allocated
Compiler: Compiled 48 359 to 4 461 computations (90.8% saved)

prune81.0ms (1.3%)

Memory

13.8MiB live, 93.0MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	2 159	2	2 161
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	2 160	6	2 166

Accuracy

100.0%

Counts

2 166 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	74.9%	(*.f64 x (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))
✓	52.3%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	51.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	3.7%	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
✓	49.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 35 to 24 computations (31.4% saved)

simplify171.0ms (2.7%)

Memory

-7.6MiB live, 107.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	(-.f64 #s(literal -1 binary64) x)
cost-diff	320	(*.f64 x (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))
cost-diff	384	(/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal -1 binary64)))
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: 0 (0.0ms)

Iter	Nodes	Cost
0	14	55
0	19	55
1	36	55
2	64	55
3	135	55
4	303	47
5	938	47
6	3095	47
7	7445	47
0	8101	45

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

localize69.0ms (1.1%)

Memory

-3.7MiB live, 33.5MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0	(-.f64 #s(literal -1 binary64) x)
accuracy	0.07421875	(*.f64 x (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))
accuracy	15.488462995733618	(/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal -1 binary64)))
accuracy	0	(*.f64 x x)
accuracy	31.10959793778832	#s(approx (+ (* x x) x) (*.f64 x x))
accuracy	31.14252889481066	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))

Samples

18.0ms

256×

valid

Compiler

Compiled 46 to 13 computations (71.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sub: 3.0ms (25.6% of total)

ival-div: 3.0ms (25.6% of total)

ival-mult: 3.0ms (25.6% of total)

ival-add: 2.0ms (17% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

6.5MiB live, 6.5MiB allocated

Counts

7 → 84

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify204.0ms (3.3%)

Memory

9.3MiB live, 200.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	473
1	125	443
2	297	428
3	1034	420
4	3964	420
5	7304	420
0	8450	388

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 81

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

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

rewrite171.0ms (2.7%)

Memory

-11.3MiB live, 273.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	52
0	19	52
1	90	52
2	677	44
0	9026	42

Stop Event

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

Counts

7 → 875

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

Outputs
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eval175.0ms (2.8%)

Memory: 24.0MiB live, 369.8MiB allocated
Compiler: Compiled 19 411 to 2 709 computations (86% saved)

prune19.0ms (0.3%)

Memory

-15.9MiB live, 70.2MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	954	2	956
Fresh	0	0	0
Picked	2	0	2
Done	0	4	4
Total	956	6	962

Accuracy

100.0%

Counts

962 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	51.6%	(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)))))
▶	51.4%	(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)))
✓	52.3%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	51.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
✓	49.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify198.0ms (3.2%)

Memory

12.3MiB live, 151.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	14	82
0	19	82
1	35	82
2	64	82
3	133	82
4	310	66
5	814	66
6	2219	66
7	4590	66
8	6895	66
9	7746	66
0	8007	66

Stop Event

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

Calls

Call 1

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

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

localize67.0ms (1.1%)

Memory

-13.1MiB live, 23.8MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 x #s(literal -1 binary64))
accuracy	0.015625	(*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)))
accuracy	0.07421875	(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)))))
accuracy	30.834081931084345	#s(approx (/ (- -1 x) (+ (* x x) -1)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64))))
accuracy	0.07421875	(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)))
accuracy	30.968174904935665	#s(approx (/ (- -1 x) (+ (* x x) -1)) #s(literal 1 binary64))

Samples

59.0ms

256×

valid

Compiler

Compiled 64 to 13 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 52.0ms

ival-div: 42.0ms (80.7% of total)

ival-mult: 4.0ms (7.7% of total)

ival-sub: 3.0ms (5.8% of total)

ival-add: 2.0ms (3.8% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

7 → 84

Calls

Call 1

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

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

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

0.0ms

-inf

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

0.0ms

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

simplify162.0ms (2.6%)

Memory

3.5MiB live, 120.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	564
1	159	520
2	462	506
3	1941	502
4	6397	502
0	8156	473

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 80

Calls

Call 1

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

rewrite190.0ms (3%)

Memory

14.6MiB live, 175.8MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	77
0	19	77
1	82	77
2	648	61
3	7472	61
0	8451	61

Stop Event

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

Counts

7 → 567

Calls

Call 1

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

Outputs
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eval92.0ms (1.5%)

Memory: -6.3MiB live, 186.5MiB allocated
Compiler: Compiled 15 594 to 2 640 computations (83.1% saved)

prune14.0ms (0.2%)

Memory

16.4MiB live, 54.6MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	647	0	647
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	647	6	653

Accuracy

100.0%

Counts

653 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	51.6%	(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)))))
✓	51.4%	(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)))
✓	52.3%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	51.3%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
✓	49.8%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 105 to 57 computations (45.7% saved)

regimes8.0ms (0.1%)

Memory

-18.4MiB live, 19.5MiB 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)))
(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)))
#s(approx (/ x (- 1 x)) (fma.f64 x 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 x #s(approx (/ (- -1 x) (+ ( x x) -1)) (*.f64 (fma.f64 x x #s(literal 1 binary64)) (-.f64 x #s(literal -1 binary64)))))
(*.f64 x (/.f64 (-.f64 #s(literal -1 binary64) x) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) x)) (.f64 (-.f64 #s(literal -1 binary64) x) (neg.f64 x))) (*.f64 (-.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 1 binary64) x)))

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

Calls

2 calls:

4.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))
3.0ms	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

13.8MiB live, 13.8MiB 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)))
(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)))
#s(approx (/ x (- 1 x)) (fma.f64 x 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:

2.0ms	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)

regimes2.0ms (0%)

Memory

6.3MiB live, 6.3MiB allocated

Counts

4 → 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)))
(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)))
#s(approx (/ x (- 1 x)) (fma.f64 x 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:

2.0ms

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

Results

Accuracy	Segments	Branch
99.0%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes22.0ms (0.4%)

Memory

-43.8MiB live, 44.0MiB 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)))
(.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)))

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

Calls

1 calls:

22.0ms

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

Results

Accuracy	Segments	Branch
97.9%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes3.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated

Counts

2 → 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)))

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

Calls

2 calls:

2.0ms	x
1.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))

Results

Accuracy	Segments	Branch
49.8%	1	`x`
51.7%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes3.0ms (0%)

Memory

7.6MiB live, 7.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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
49.8%	1	`x`
49.8%	1	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

bsearch0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-3.0115435560255752e-5

Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-1.0	-3.0115435560255752e-5

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	-1.0	-3.0115435560255752e-5

Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.0843000462287942e-151	-3.383271805999834e-157

Compiler

Compiled 8 to 8 computations (0% saved)

simplify124.0ms (2%)

Memory

8.7MiB live, 46.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	123
1	35	123
2	38	123
3	40	123
4	41	123

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 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 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 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -2948408144391829/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496 binary64)) #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)) #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 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 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 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (.f64 x #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64))))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) #s(approx (/ x (- 1 x)) #s(literal -1 binary64)) (.f64 #s(approx (/ (- -1 x) (+ ( x x) -1)) #s(literal 1 binary64)) x))
(if (<=.f64 (/.f64 x (-.f64 #s(literal 1 binary64) x)) #s(literal -2948408144391829/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496 binary64)) #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)) #s(literal -1 binary64))

soundness1.6s (24.8%)

Memory

-4.3MiB live, 670.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	473
1	125	443
2	297	428
3	1034	420
4	3964	420
5	7304	420
0	8450	388
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
0	4	8
0	6	8
1	29	8
2	183	8
3	1612	8
0	9347	8
0	38	652
1	118	628
2	323	600
3	1018	592
4	3587	592
5	7193	592
0	8754	538
0	19	81
0	31	71
1	133	68
2	1003	58
0	9010	57

Stop Event

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

Compiler

Compiled 125 to 57 computations (54.4% saved)

preprocess61.0ms (1%)

Memory: 5.4MiB live, 117.9MiB allocated
Compiler: Compiled 148 to 52 computations (64.9% 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	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

start0.0ms (0%)

analyze1.0ms (0%)

sample683.0ms (10.9%)

explain58.0ms (0.9%)

preprocess29.0ms (0.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize16.0ms (0.3%)

series2.0ms (0%)

simplify149.0ms (2.4%)

rewrite169.0ms (2.7%)

eval184.0ms (2.9%)

prune8.0ms (0.1%)

simplify424.0ms (6.8%)

localize98.0ms (1.6%)

series10.0ms (0.2%)

simplify169.0ms (2.7%)

rewrite304.0ms (4.9%)

eval551.0ms (8.8%)

prune81.0ms (1.3%)

simplify171.0ms (2.7%)

localize69.0ms (1.1%)

series4.0ms (0.1%)

simplify204.0ms (3.3%)

rewrite171.0ms (2.7%)

eval175.0ms (2.8%)

prune19.0ms (0.3%)

simplify198.0ms (3.2%)

localize67.0ms (1.1%)

series4.0ms (0.1%)

simplify162.0ms (2.6%)

rewrite190.0ms (3%)

eval92.0ms (1.5%)

prune14.0ms (0.2%)

regimes8.0ms (0.1%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes22.0ms (0.4%)

regimes3.0ms (0.1%)

regimes3.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify124.0ms (2%)

soundness1.6s (24.8%)

preprocess61.0ms (1%)

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