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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

1.8MiB live, 1.8MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
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)

sample722.0ms (18.3%)

Memory

-9.2MiB live, 639.6MiB allocated

Samples

415.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 210.0ms

ival-sub: 122.0ms (58.2% of total)

ival-div: 73.0ms (34.8% of total)

ival-true: 6.0ms (2.9% of total)

exact: 5.0ms (2.4% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

explain60.0ms (1.5%)

Memory

9.2MiB live, 87.7MiB 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

38.0ms

512×

valid

Compiler

Compiled 39 to 20 computations (48.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-div: 5.0ms (58.4% of total)

ival-sub: 3.0ms (35.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess58.0ms (1.5%)

Memory

-37.9MiB live, 16.1MiB 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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB 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

2.3MiB live, 2.3MiB 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)

localize13.0ms (0.3%)

Memory

13.6MiB live, 13.6MiB 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

8.0ms

256×

valid

Compiler

Compiled 22 to 10 computations (54.5% saved)

Precisions

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

ival-div: 2.0ms (54.1% of total)

ival-sub: 1.0ms (27% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

2.7MiB live, 2.7MiB allocated

Counts

2 → 24

Calls

Call 1

Inputs
#s(alt #<batchref> (patch (/.f64 x (-.f64 #s(literal 1 binary64) x)) #<representation binary64>) () ())
#s(alt #<batchref> (patch (-.f64 #s(literal 1 binary64) x) #<representation binary64>) () ())

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

simplify256.0ms (6.5%)

Memory

-8.2MiB live, 66.9MiB 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
(fma.f64 x x x)
(fma.f64 (fma.f64 x x x) x x)
(*.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) x) (-.f64 x #s(literal -1 binary64)))
#s(literal 1 binary64)
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 1 binary64) x)
#s(literal -1 binary64)
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) 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)))
(neg.f64 x)
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 1 binary64) x)
#s(literal -1 binary64)
(-.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) x))
(-.f64 #s(literal -1 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) 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)))
(neg.f64 x)
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 1 binary64) x)
(-.f64 #s(literal 1 binary64) x)

rewrite320.0ms (8.1%)

Memory

10.8MiB live, 290.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

2 → 425

Calls

Call 1

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

Outputs
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eval181.0ms (4.6%)

Memory: 5.2MiB live, 163.9MiB allocated
Compiler: Compiled 10 317 to 1 292 computations (87.5% saved)

prune10.0ms (0.2%)

Memory

-0.7MiB live, 36.7MiB 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
▶	76.5%	(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
▶	50.2%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
▶	49.2%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	51.0%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 46 to 30 computations (34.8% saved)

simplify149.0ms (3.8%)

Memory

-0.1MiB live, 159.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	78
0	21	78
1	39	78
2	86	78
3	213	72
4	502	72
5	1704	72
6	6009	72
0	8070	71

Stop Event

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

Calls

Call 1

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

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

localize39.0ms (1%)

Memory

9.1MiB live, 44.3MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(neg.f64 (fma.f64 x x x))
accuracy	0.0078125	(+.f64 #s(literal -1 binary64) (*.f64 x x))
accuracy	14.914279192440134	(/.f64 (neg.f64 (fma.f64 x x x)) (+.f64 #s(literal -1 binary64) (*.f64 x x)))
accuracy	0	(fma.f64 x x x)
accuracy	0.04296875	(fma.f64 (fma.f64 x x x) x x)
accuracy	31.893350482985575	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
accuracy	0	(fma.f64 x x x)
accuracy	32.541947824765295	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
accuracy	31.37954679484949	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Samples

29.0ms

256×

valid

Compiler

Compiled 150 to 28 computations (81.3% saved)

Precisions

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

ival-div: 3.0ms (22.8% of total)

ival-add: 3.0ms (22.8% of total)

ival-mult: 3.0ms (22.8% of total)

ival-sub: 2.0ms (15.2% of total)

ival-neg: 1.0ms (7.6% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Counts

9 → 108

Calls

Call 1

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

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

Calls

3 calls:

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

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify165.0ms (4.2%)

Memory

-30.2MiB live, 251.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 102

Calls

Call 1

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

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

rewrite153.0ms (3.9%)

Memory

0.5MiB live, 194.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	65
0	21	65
1	96	59
2	702	59
0	8322	58

Stop Event

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

Counts

9 → 793

Calls

Call 1

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

Outputs
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eval204.0ms (5.2%)

Memory: 39.5MiB live, 275.7MiB allocated
Compiler: Compiled 26 989 to 2 671 computations (90.1% saved)

prune26.0ms (0.7%)

Memory

2.4MiB live, 74.9MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	1 217	2	1 219
Fresh	0	0	0
Picked	1	3	4
Done	0	1	1
Total	1 218	6	1 224

Accuracy

100.0%

Counts

1 224 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	76.5%	(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	50.2%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	49.2%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
▶	3.3%	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
✓	51.0%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 60 to 38 computations (36.7% saved)

simplify150.0ms (3.8%)

Memory

4.8MiB live, 166.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	12	50
0	16	50
1	27	50
2	39	50
3	58	50
4	84	50
5	154	50
6	393	45
7	1504	45
8	3406	45
9	6793	45
0	8068	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 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
(fma.f64 x x x)
x
(-.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)
(*.f64 x x)

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

localize50.0ms (1.3%)

Memory

-4.1MiB live, 75.2MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(fma.f64 x x x)
accuracy	0	(*.f64 x x)
accuracy	0.0078125	(-.f64 #s(literal 1 binary64) (*.f64 x x))
accuracy	14.914279192440134	(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
accuracy	0	(*.f64 x x)
accuracy	30.803765894392036	#s(approx (+ (* x x) x) (*.f64 x x))
accuracy	32.541947824765295	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))

Samples

16.0ms

256×

valid

Compiler

Compiled 94 to 23 computations (75.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-sub: 3.0ms (32.7% of total)

ival-div: 3.0ms (32.7% of total)

ival-mult: 2.0ms (21.8% of total)

ival-add: 1.0ms (10.9% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

-31.0MiB live, 6.2MiB allocated

Counts

6 → 72

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

0.0ms

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

simplify165.0ms (4.2%)

Memory

17.6MiB live, 218.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	391
1	92	370
2	220	358
3	532	354
4	1394	354
5	4307	354
6	7825	354
0	8157	326

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 68

Calls

Call 1

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

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

rewrite210.0ms (5.3%)

Memory

-16.3MiB live, 147.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	44
0	16	44
1	71	39
2	509	39
3	5819	39
0	9500	38

Stop Event

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

Counts

6 → 575

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

Outputs
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eval90.0ms (2.3%)

Memory: 4.3MiB live, 154.3MiB allocated
Compiler: Compiled 12 500 to 1 393 computations (88.9% saved)

prune17.0ms (0.4%)

Memory

-1.9MiB live, 49.0MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	674	0	674
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	674	6	680

Accuracy

100.0%

Counts

680 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	76.5%	(/.f64 (fma.f64 x x x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))
✓	100.0%	(/.f64 x (-.f64 #s(literal 1 binary64) x))
✓	50.2%	#s(approx (/ x (- 1 x)) (fma.f64 (fma.f64 x x x) x x))
✓	49.2%	#s(approx (/ x (- 1 x)) (fma.f64 x x x))
✓	3.3%	#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
✓	51.0%	#s(approx (/ x (- 1 x)) #s(literal -1 binary64))

Compiler

Compiled 131 to 61 computations (53.4% saved)

regimes6.0ms (0.2%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes5.0ms (0.1%)

Memory

10.1MiB live, 10.1MiB 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)))
#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
98.0%	3	`x`
98.0%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 6 to 5 computations (16.7% saved)

regimes2.0ms (0%)

Memory

4.6MiB live, 4.6MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (/ x (- 1 x)) #s(literal -1 binary64))
#s(approx (/ x (- 1 x)) #s(approx (+ (* x x) x) (*.f64 x x)))
#s(approx (/ x (- 1 x)) (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
97.7%	2	`(/.f64 x (-.f64 #s(literal 1 binary64) x))`

Compiler

Compiled 5 to 4 computations (20% saved)

regimes6.0ms (0.1%)

Memory

-30.7MiB live, 8.1MiB allocated

Accuracy

Total -31.5b remaining (-100.2%)

Threshold costs -31.5b (-100.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	(/.f64 x (-.f64 #s(literal 1 binary64) x))
2.0ms	x

Results

Accuracy	Segments	Branch
51.0%	1	`x`
51.0%	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	-0.9999999770258328	-0.04486257597375225

Compiler

Compiled 8 to 8 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-0.9999999770258328	-0.04486257597375225

Compiler

Compiled 8 to 8 computations (0% saved)

simplify46.0ms (1.2%)

Memory

6.1MiB live, 45.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	65
1	21	65
2	24	65
3	26	65
4	27	65

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness783.0ms (19.9%)

Memory

-13.3MiB live, 152.4MiB allocated

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×	done
1×	iter limit
1×	saturated

Compiler

Compiled 79 to 28 computations (64.6% saved)

preprocess32.0ms (0.8%)

Memory: -2.8MiB live, 77.2MiB allocated
Compiler: Compiled 140 to 42 computations (70% 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%)

sample722.0ms (18.3%)

explain60.0ms (1.5%)

preprocess58.0ms (1.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize13.0ms (0.3%)

series1.0ms (0%)

simplify256.0ms (6.5%)

rewrite320.0ms (8.1%)

eval181.0ms (4.6%)

prune10.0ms (0.2%)

simplify149.0ms (3.8%)

localize39.0ms (1%)

series5.0ms (0.1%)

simplify165.0ms (4.2%)

rewrite153.0ms (3.9%)

eval204.0ms (5.2%)

prune26.0ms (0.7%)

simplify150.0ms (3.8%)

localize50.0ms (1.3%)

series5.0ms (0.1%)

simplify165.0ms (4.2%)

rewrite210.0ms (5.3%)

eval90.0ms (2.3%)

prune17.0ms (0.4%)

regimes6.0ms (0.2%)

regimes5.0ms (0.1%)

regimes2.0ms (0%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify46.0ms (1.2%)

soundness783.0ms (19.9%)

preprocess32.0ms (0.8%)

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