Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB 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
100%	100%	0%	0%	0%	0%	0%	2

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample1.0s (17%)

Memory

28.7MiB live, 624.5MiB allocated

Samples

648.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 202.0ms

ival-div: 71.0ms (35.1% of total)

ival-mult: 71.0ms (35.1% of total)

ival-add: 46.0ms (22.8% of total)

ival-true: 6.0ms (3% of total)

exact: 5.0ms (2.5% of total)

ival-assert: 3.0ms (1.5% of total)

Bogosity

explain96.0ms (1.6%)

Memory

3.7MiB live, 93.9MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
61	-	-	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
0	-	-	`#s(literal 1 binary64)`
0	-	-	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`/.f64`	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`	n/o	61	0
↳	`(*.f64 x x)`	overflow	61
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	61

Confusion

	Predicted +	Predicted -
+	61	0
-	0	195

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	61	0	0
-	0	0	195

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	195
1	61

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

48.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-mult: 28.0ms (78.2% of total)

ival-div: 4.0ms (11.2% of total)

ival-add: 3.0ms (8.4% of total)

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

exact: 0.0ms (0% of total)

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

preprocess17.0ms (0.3%)

Memory

16.7MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	24	15
2	56	14
3	71	14
4	91	14
0	5	7
0	8	7
1	15	7
2	34	7
3	61	7
4	78	7
5	81	7
6	89	7
7	91	7
0	91	6

Stop Event

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

Calls

Call 1

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

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

Symmetry

(negabs x)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	77.6%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify5.0ms (0.1%)

Memory

3.8MiB live, 3.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	15	17
2	34	17
3	61	17
4	78	17
5	81	17
6	89	17
7	91	17
0	91	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize20.0ms (0.3%)

Memory

-20.7MiB live, 23.7MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (*.f64 x x) #s(literal 1 binary64))
accuracy	0.0	(*.f64 x x)
accuracy	14.307739495917595	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Samples

15.0ms

256×

valid

Compiler

Compiled 19 to 7 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-div: 2.0ms (33.2% of total)

ival-mult: 2.0ms (33.2% of total)

ival-add: 1.0ms (16.6% 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

3.5MiB live, 3.4MiB allocated

Counts

3 → 15

Calls

Call 1

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

Outputs
1
(+ 1 (pow x 2))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))

Calls

3 calls:

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

simplify141.0ms (2.4%)

Memory

7.2MiB live, 155.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	152
1	128	150
2	336	142
3	1106	140
4	2977	137
5	7066	135
0	8174	131

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 14

Calls

Call 1

Inputs
1
(+ 1 (pow x 2))
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))

Outputs
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #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))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (-.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) x)
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) (+.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) x)
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))) (neg.f64 x))

rewrite222.0ms (3.8%)

Memory

3.5MiB live, 143.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	33	15
2	220	15
3	2396	15
0	9401	13

Stop Event

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

Counts

3 → 236

Calls

Call 1

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

Outputs
(*.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64))))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (neg.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)))) (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64)) (-.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (neg.f64 (fma.f64 (fma.f64 x x #s(literal 1 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1 binary64))) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)))
(*.f64 (neg.f64 (-.f64 x #s(literal 1 binary64))) (-.f64 #s(literal 1 binary64) x))
(*.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))
(*.f64 (-.f64 x #s(literal 1 binary64)) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(*.f64 (-.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) x))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (tanh.f64 (log.f64 x)))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (neg.f64 (tanh.f64 (log.f64 x))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))))
(*.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64))) (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (-.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -3 binary64)) (/.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64)) (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)))) (fma.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 x x #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64)))))))
(/.f64 (+.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -3 binary64)) (/.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -2 binary64)) (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (*.f64 (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)) (/.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))))))
(/.f64 (neg.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -3 binary64)))) (neg.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) #s(literal 2 binary64)) (-.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -2 binary64)) (*.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal -1 binary64)))))))
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(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))

eval30.0ms (0.5%)

Memory: 6.6MiB live, 51.2MiB allocated
Compiler: Compiled 6 534 to 801 computations (87.7% saved)

prune8.0ms (0.1%)

Memory

-27.3MiB live, 19.4MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	244	5	249
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	245	5	250

Accuracy

100.0%

Counts

250 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.1%	(/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
▶	77.6%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	52.8%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x))
▶	49.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 110 to 78 computations (29.1% saved)

simplify169.0ms (2.9%)

Memory

19.3MiB live, 161.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 14 expressions of interest:

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	112
0	34	112
1	62	112
2	188	110
3	833	110
4	2494	110
5	7081	110
0	8446	110

Stop Event

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

Calls

Call 1

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

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

localize231.0ms (3.9%)

Memory

4.9MiB live, 51.7MiB allocated

Localize:

Found 14 expressions of interest:

New	Metric	Score
accuracy	0.0	(pow.f64 x #s(literal 4 binary64))
accuracy	0.0	(-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))
accuracy	0.04296875	(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
accuracy	22.527769760708782	(/.f64 (*.f64 x (fma.f64 x x #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64)))
accuracy	0.0	(fma.f64 x x #s(literal -1 binary64))
accuracy	0.0	(pow.f64 x #s(literal 3 binary64))
accuracy	0.03515625	(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x)
accuracy	30.214999686859606	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x))
accuracy	14.307739495917595	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
accuracy	30.044064301459844	#s(approx (+ (* x x) 1) #s(literal 1 binary64))
accuracy	0.0	(/.f64 #s(literal 1 binary64) x)
accuracy	32.15983561531664	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
accuracy	0.0	(fma.f64 x x #s(literal 1 binary64))
accuracy	14.307739495917595	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))

Samples

219.0ms

256×

valid

Compiler

Compiled 108 to 19 computations (82.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 207.0ms

ival-pow: 191.0ms (92.3% of total)

ival-div: 5.0ms (2.4% of total)

ival-mult: 5.0ms (2.4% of total)

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

ival-sub: 1.0ms (0.5% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

8.6MiB live, 8.6MiB allocated

Counts

14 → 31

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
1
(+ 1 (pow x 2))
(/ 1 x)
(pow x 3)
-1
(- (pow x 2) 1)
(* -1 x)
(* x (- (pow x 2) 1))
(- (pow x 4) 1)
(pow x 4)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 5)
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* (pow x 3) (+ (* x x) -1)) x) (pow x 3) (+ (* x x) -1) (* x (+ (* x x) -1)) (/ (* x (+ (* x x) -1)) (- (pow x 4) 1)) (- (pow x 4) 1) (pow x 4))
2.0ms	x	@	inf	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* (pow x 3) (+ (* x x) -1)) x) (pow x 3) (+ (* x x) -1) (* x (+ (* x x) -1)) (/ (* x (+ (* x x) -1)) (- (pow x 4) 1)) (- (pow x 4) 1) (pow x 4))
2.0ms	x	@	0	((/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (/ 1 x) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* (pow x 3) (+ (* x x) -1)) x) (pow x 3) (+ (* x x) -1) (* x (+ (* x x) -1)) (/ (* x (+ (* x x) -1)) (- (pow x 4) 1)) (- (pow x 4) 1) (pow x 4))

Time

Variable

Point

Expression

2.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

simplify332.0ms (5.6%)

Memory

14.7MiB live, 158.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	284
1	171	274
2	409	274
3	1284	271
4	3374	264
5	7811	261
0	8533	256

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 30

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
1
(+ 1 (pow x 2))
(/ 1 x)
(pow x 3)
-1
(- (pow x 2) 1)
(* -1 x)
(* x (- (pow x 2) 1))
(- (pow x 4) 1)
(pow x 4)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(pow x 5)
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #s(literal -1 binary64)) x)
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (pow x 2) 1))
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(- (pow x 4) 1)
(-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #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 5)
(pow.f64 x #s(literal 5 binary64))
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal -1 binary64)))
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) x) x)
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) (pow.f64 x #s(literal 3 binary64)))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))) (neg.f64 x))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))

rewrite347.0ms (5.9%)

Memory

-13.0MiB live, 224.5MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	95
0	34	95
1	130	95
2	888	93
0	9606	93

Stop Event

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

Counts

14 → 692

Calls

Call 1

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

Outputs
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64))) (-.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(*.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal -1 binary64)))
(/.f64 (.f64 x (-.f64 (pow.f64 x #s(literal 8 binary64)) (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 x x #s(literal 1 binary64)))))
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(pow.f64 x #s(literal 4 binary64))
(/.f64 (-.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))) (-.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))))))
(neg.f64 (pow.f64 x #s(literal 4 binary64)))
(fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64) (.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64)))
(fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (neg.f64 x) (.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))) (neg.f64 x)))
(fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) x (.f64 (sinh.f64 (*.f64 (log.f64 x) #s(literal 3 binary64))) x))
(fma.f64 (neg.f64 x) (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (.f64 (neg.f64 x) (sinh.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))))
(fma.f64 #s(literal 1 binary64) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (.f64 #s(literal 1 binary64) (sinh.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))))
(fma.f64 x (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (.f64 x (sinh.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))))
(sqrt.f64 (pow.f64 x #s(literal 8 binary64)))
(fabs.f64 (pow.f64 x #s(literal 4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(+.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (neg.f64 x)) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) (neg.f64 x)))
(+.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) x) (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64))) x))
(+.f64 (.f64 (neg.f64 x) (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))) (.f64 (neg.f64 x) (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))))
(+.f64 (.f64 #s(literal 1 binary64) (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (.f64 #s(literal 1 binary64) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))))
(+.f64 (.f64 x (cosh.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))) (.f64 x (sinh.f64 (.f64 (log.f64 x) #s(literal 3 binary64)))))
(+.f64 (neg.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))) (neg.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64)))))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 4 binary64))))

eval105.0ms (1.8%)

Memory: 19.6MiB live, 162.1MiB allocated
Compiler: Compiled 19 229 to 2 267 computations (88.2% saved)

prune103.0ms (1.7%)

Memory

-10.8MiB live, 33.4MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	794	3	797
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	796	6	802

Accuracy

100.0%

Counts

802 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	64.1%	(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))
✓	77.6%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	27.3%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	52.8%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x x))
✓	49.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 71 to 44 computations (38% saved)

simplify300.0ms (5.1%)

Memory

6.3MiB live, 187.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	1	(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
cost-diff	3	(fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))
cost-diff	5	(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (+ (* x x) 1) (*.f64 x x))
cost-diff	0	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
cost-diff	0	(fma.f64 x x #s(literal -1 binary64))
cost-diff	0	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x x))
cost-diff	1	(.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x))
cost-diff	1	(fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	109
0	26	109
1	63	105
2	229	94
3	1249	92
4	6050	92
0	8178	88

Stop Event

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

Calls

Call 1

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

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

localize71.0ms (1.2%)

Memory

-35.9MiB live, 70.4MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 x x)
accuracy	0.04296875	(*.f64 x (fma.f64 x x #s(literal -1 binary64)))
accuracy	0.06478500976844201	(fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))
accuracy	22.527769760708782	(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	14.307739495917595	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
accuracy	32.02895412044952	#s(approx (+ (* x x) 1) (*.f64 x x))
accuracy	0.0	(*.f64 x x)
accuracy	0.01171875	(fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x x)
accuracy	0.060878759768442016	(.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x))
accuracy	30.214999686859606	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x x))

Samples

40.0ms

256×

valid

Compiler

Compiled 100 to 16 computations (84% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 8.0ms (49.6% of total)

ival-add: 5.0ms (31% of total)

ival-div: 3.0ms (18.6% 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

5.5MiB live, 5.5MiB allocated

Counts

10 → 34

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* -1 (pow x 2))
(* (pow x 2) (- (pow x 2) 1))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
-1
(- (pow x 2) 1)
1
(+ 1 (pow x 2))
(pow x 2)
(- (pow x 4) 1)
(* -1 x)
(* x (- (pow x 2) 1))
(pow x 5)
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(pow x 3)
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

inf

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

1.0ms

-inf

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

1.0ms

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

simplify168.0ms (2.9%)

Memory

-4.5MiB live, 159.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	308
1	173	298
2	411	298
3	1289	294
4	3369	286
5	7858	283
0	8580	278

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 33

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* -1 (pow x 2))
(* (pow x 2) (- (pow x 2) 1))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
-1
(- (pow x 2) 1)
1
(+ 1 (pow x 2))
(pow x 2)
(- (pow x 4) 1)
(* -1 x)
(* x (- (pow x 2) 1))
(pow x 5)
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 2))))
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(pow x 3)
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (pow x 2) 1))
(fma.f64 (neg.f64 x) x (pow.f64 x #s(literal 4 binary64)))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #s(literal -1 binary64)) x)
-1
#s(literal -1 binary64)
(- (pow x 2) 1)
(fma.f64 x x #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (pow x 2))
(fma.f64 x x #s(literal 1 binary64))
(pow x 2)
(*.f64 x x)
(- (pow x 4) 1)
(-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))
(* -1 x)
(neg.f64 x)
(* x (- (pow x 2) 1))
(-.f64 (pow.f64 x #s(literal 3 binary64)) x)
(pow x 5)
(pow.f64 x #s(literal 5 binary64))
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) (pow.f64 x #s(literal 5 binary64)))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(*.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) (pow.f64 x #s(literal 5 binary64)))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 2))))
(.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/.f64 (+.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) #s(literal 1 binary64)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64))) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64))) x)
(* (pow x 2) (- 1 (/ 1 (pow x 2))))
(.f64 (.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x))) x) x)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(fma.f64 x x #s(literal 1 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 4))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))))
(pow x 3)
(pow.f64 x #s(literal 3 binary64))
(* (pow x 3) (- 1 (/ 1 (pow x 2))))
(.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) x) x) (pow.f64 (neg.f64 x) #s(literal 3 binary64)))) (neg.f64 x))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1)))
(.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)))

rewrite212.0ms (3.6%)

Memory

-11.6MiB live, 122.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	94
0	26	92
1	115	86
2	882	78
0	9981	74

Stop Event

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

Counts

10 → 771

Calls

Call 1

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

Outputs
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 1 binary64))) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x) x))
(*.f64 (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x) x) (/.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x) (fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 1 binary64))))
(*.f64 (fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 1 binary64)) x)
(*.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x #s(literal 1 binary64)))
(*.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x #s(literal -1 binary64)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))) (.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))))) (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (fma.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (*.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))))) (.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))))))))
(/.f64 (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x) (.f64 x x))) (fma.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (*.f64 x x)))
(/.f64 (fma.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))) (.f64 (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))) (pow.f64 x #s(literal 3 binary64)))) (-.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 4 binary64)) (pow.f64 (.f64 x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) #s(literal 2 binary64))))
(/.f64 (fma.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64)) (*.f64 x x)) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))
(/.f64 (fma.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (neg.f64 (*.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (*.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))))
(/.f64 (fma.f64 (pow.f64 (fma.f64 x x #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 9 binary64)) (pow.f64 x #s(literal 3 binary64))) (*.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))))
(neg.f64 (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x))
(fma.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 x))
(fma.f64 (*.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))) (-.f64 (neg.f64 x) #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))) (-.f64 (neg.f64 x) #s(literal 1 binary64)) x)
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x) (neg.f64 x))
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x) x)
(fma.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (.f64 x x) (neg.f64 x))
(fma.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (.f64 x x) x)
(fma.f64 (.f64 (.f64 x x) (fma.f64 x x x)) (-.f64 x #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (.f64 (.f64 x x) (fma.f64 x x x)) (-.f64 x #s(literal 1 binary64)) x)
(fma.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) (neg.f64 x))
(fma.f64 (*.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 x #s(literal 3/2 binary64)) x)
(fma.f64 (*.f64 x (fma.f64 x x (pow.f64 x #s(literal 3 binary64)))) (-.f64 x #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (*.f64 x (fma.f64 x x (pow.f64 x #s(literal 3 binary64)))) (-.f64 x #s(literal 1 binary64)) x)
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (*.f64 (pow.f64 x #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)) x)
(fma.f64 (*.f64 (neg.f64 x) (fma.f64 x x (pow.f64 x #s(literal 3 binary64)))) (-.f64 x #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (*.f64 (neg.f64 x) (fma.f64 x x (pow.f64 x #s(literal 3 binary64)))) (-.f64 x #s(literal 1 binary64)) x)
(fma.f64 (.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) x)) (.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) x) (neg.f64 x))
(fma.f64 (.f64 (neg.f64 x) (+.f64 #s(literal 1 binary64) x)) (.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) x) x) x)
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 x))
(fma.f64 (neg.f64 (+.f64 #s(literal 1 binary64) x)) (*.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) x)
(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 (sqrt.f64 x) (sqrt.f64 x) (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 3 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) x) (neg.f64 x))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 3 binary64))) (*.f64 (-.f64 x #s(literal 1 binary64)) x) x)
(fma.f64 (fma.f64 x x x) (.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) x) (neg.f64 x))
(fma.f64 (fma.f64 x x x) (.f64 (.f64 (-.f64 x #s(literal 1 binary64)) x) x) x)
(fma.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 x))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (neg.f64 (*.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) x)
(fma.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 x))
(fma.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 (-.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) (neg.f64 x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) (neg.f64 x))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x)
(fma.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))
(fma.f64 (fma.f64 x x #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 (neg.f64 x) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (neg.f64 x))
(fma.f64 (neg.f64 x) (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) x)
(fma.f64 (neg.f64 x) #s(literal -1 binary64) (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 (*.f64 (neg.f64 x) x) (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (neg.f64 x))
(fma.f64 (*.f64 (neg.f64 x) x) (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x)
(fma.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64) (neg.f64 x))
(fma.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64) x)
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (*.f64 (neg.f64 x) x) (neg.f64 x))
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (*.f64 (neg.f64 x) x) x)
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (*.f64 x x) (neg.f64 x))
(fma.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (*.f64 x x) x)
(fma.f64 #s(literal 1 binary64) x (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (neg.f64 x) (neg.f64 x))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (neg.f64 x) x)
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) x (neg.f64 x))
(fma.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) x x)
(fma.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) x) (neg.f64 x))
(fma.f64 (*.f64 x x) (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x)
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))
(fma.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 3 binary64)) x)
(fma.f64 #s(literal -1 binary64) (neg.f64 x) (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 x #s(literal 1 binary64) (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))))
(fma.f64 x (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (neg.f64 x))
(fma.f64 x (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) x)
(-.f64 (/.f64 (pow.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (.f64 x (fma.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 x #s(literal 4 binary64))) x (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))))
(-.f64 (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)) (/.f64 (.f64 x x) (fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal 1 binary64)) x)))
(-.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 x))
(-.f64 (+.f64 (pow.f64 x #s(literal 5 binary64)) (pow.f64 x #s(literal 3 binary64))) x)
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(fma.f64 (sqrt.f64 (neg.f64 x)) (sqrt.f64 (neg.f64 x)) (pow.f64 x #s(literal 3 binary64)))
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(+.f64 (pow.f64 x #s(literal 3 binary64)) (neg.f64 x))
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eval170.0ms (2.9%)

Memory: 17.6MiB live, 256.5MiB allocated
Compiler: Compiled 23 571 to 2 721 computations (88.5% saved)

prune26.0ms (0.4%)

Memory

4.5MiB live, 49.7MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	987	1	988
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	987	7	994

Accuracy

100.0%

Counts

994 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	64.1%	(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))
✓	77.6%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	27.3%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	52.8%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x x))
▶	51.9%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 (neg.f64 x) x)) x x))
✓	49.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 96 to 57 computations (40.6% saved)

simplify203.0ms (3.4%)

Memory

23.3MiB live, 253.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	63
0	17	63
1	36	63
2	97	63
3	348	57
4	1457	57
5	3244	57
6	6092	57
0	8538	56

Stop Event

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

Calls

Call 1

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

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

localize93.0ms (1.6%)

Memory

-22.1MiB live, 24.9MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(neg.f64 x)
accuracy	0.01171875	(fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 (neg.f64 x) x)) x x)
accuracy	30.214999686859606	#s(approx (/ x (+ (* x x) 1)) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 (neg.f64 x) x)) x x))
accuracy	31.300480295010505	#s(approx (* (+ (* x x) -1) (* x x)) (*.f64 (neg.f64 x) x))

Samples

86.0ms

256×

valid

Compiler

Compiled 38 to 14 computations (63.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-mult: 73.0ms (91.8% of total)

ival-add: 3.0ms (3.8% of total)

ival-div: 2.0ms (2.5% of total)

ival-neg: 1.0ms (1.3% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

1.9MiB live, 1.9MiB allocated

Counts

5 → 21

Calls

Call 1

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

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(* -1 (pow x 2))
(* (pow x 2) (- (pow x 2) 1))
(* -1 x)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(pow x 5)
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 2))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify326.0ms (5.5%)

Memory

-21.9MiB live, 139.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	228
1	142	226
2	345	218
3	1051	215
4	2837	209
5	6669	209
0	8270	207

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 20

Calls

Call 1

Inputs
x
(* x (+ 1 (* -1 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(* -1 (pow x 2))
(* (pow x 2) (- (pow x 2) 1))
(* -1 x)
(/ 1 x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(pow x 5)
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(pow x 4)
(* (pow x 4) (- 1 (/ 1 (pow x 2))))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))

Outputs
x
(* x (+ 1 (* -1 (pow x 2))))
(-.f64 x (pow.f64 x #s(literal 3 binary64)))
(* x (+ 1 (* (pow x 2) (- (pow x 2) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x #s(literal -1 binary64)) x)
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1 (* -1 (pow x 2)))) 1))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (-.f64 x (pow.f64 x #s(literal 3 binary64))) x #s(literal -1 binary64)) x)
(* -1 (pow x 2))
(*.f64 (neg.f64 x) x)
(* (pow x 2) (- (pow x 2) 1))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) x) x)
(* -1 x)
(neg.f64 x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (/ 1 (pow x 2))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)) x)
(/ (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))) x)
(-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) x))
(/ (- (+ 1 (/ 1 (pow x 4))) (+ (/ 1 (pow x 2)) (/ 1 (pow x 6)))) x)
(/.f64 (-.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) x)
(pow x 5)
(pow.f64 x #s(literal 5 binary64))
(* (pow x 5) (- 1 (/ 1 (pow x 2))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)))
(* (pow x 5) (- (+ 1 (/ 1 (pow x 4))) (/ 1 (pow x 2))))
(*.f64 (pow.f64 x #s(literal 5 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))) (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64))))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(* (pow x 4) (- 1 (/ 1 (pow x 2))))
(*.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) x)))
(* -1 (/ (- (/ 1 (pow x 2)) 1) x))
(/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x)
(* -1 (/ (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4)))) x))
(-.f64 (/.f64 (+.f64 (/.f64 #s(literal -1 binary64) (*.f64 x x)) #s(literal 1 binary64)) x) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64))))
(* -1 (/ (- (+ (/ 1 (pow x 2)) (/ 1 (pow x 6))) (+ 1 (/ 1 (pow x 4)))) x))
(/.f64 (-.f64 (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))) (-.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64))))) x)
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) 1)))
(.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (pow.f64 x #s(literal 5 binary64)))
(* -1 (* (pow x 5) (- (/ 1 (pow x 2)) (+ 1 (/ 1 (pow x 4))))))
(.f64 (-.f64 (-.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 5 binary64)))

rewrite140.0ms (2.4%)

Memory

28.0MiB live, 223.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	62
0	17	62
1	74	62
2	496	56
3	5666	51
0	9378	47

Stop Event

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

Counts

5 → 112

Calls

Call 1

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

Outputs
#s(approx (/ x (+ (* x x) 1)) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 x x)) x x))
(.f64 (/.f64 (.f64 (+.f64 (pow.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x)) #s(literal 2 binary64))) (fma.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x)))
(.f64 (/.f64 (.f64 (+.f64 (pow.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (pow.f64 (+.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 1 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)) (pow.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 6 binary64)))) (fma.f64 (.f64 (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x x) x) (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x)) (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x) #s(literal 4 binary64))))
(.f64 (/.f64 (pow.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) #s(literal 2 binary64)) (pow.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) #s(literal 2 binary64))) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x x))
(.f64 (/.f64 (pow.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) #s(literal 2 binary64)) (.f64 (+.f64 (pow.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))))
(.f64 (/.f64 (pow.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) #s(literal 2 binary64)) (.f64 (+.f64 (pow.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x)))
(.f64 (/.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (+.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 1 binary64))) (/.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x x) x))
(.f64 (/.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) x) (/.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (+.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64))))
(.f64 (+.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64)) x)
(.f64 (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x)) (/.f64 (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))))
(.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (/.f64 (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x x)))
(.f64 x (+.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (/.f64 (pow.f64 (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x x) #s(literal 2 binary64)) (+.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64))) x)
(/.f64 (/.f64 (pow.f64 (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x x) #s(literal 2 binary64)) x) (+.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (.f64 (-.f64 (pow.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64)) x) (-.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (.f64 (+.f64 (pow.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64)) x) (+.f64 (-.f64 #s(literal 1 binary64) #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x))) (pow.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 2 binary64))))
(/.f64 (.f64 x (-.f64 (pow.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (.f64 x (+.f64 (pow.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) #s(literal 3 binary64)) #s(literal 1 binary64))) (+.f64 (-.f64 #s(literal 1 binary64) #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x))) (pow.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 2 binary64)) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x)) #s(literal 2 binary64)) (pow.f64 (/.f64 (.f64 x x) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x x)) #s(literal 2 binary64))) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x x))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))) #s(literal 2 binary64))) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 x x)) x x))
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(fma.f64 x #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 x x)) x)
(fma.f64 x #s(literal 1 binary64) (.f64 (neg.f64 (neg.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)))) x))
(fma.f64 x #s(literal 1 binary64) (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))))
(-.f64 (/.f64 (.f64 x x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x)) (/.f64 (pow.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 2 binary64)) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x x)))
(-.f64 (/.f64 (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 2 binary64)) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x)) (/.f64 (.f64 x x) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 x x)) x x)))
(-.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x) x)
(-.f64 x (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x))
(+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))) (/.f64 (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x) (.f64 x x))))
(+.f64 (/.f64 (pow.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x) #s(literal 2 binary64)) (fma.f64 #s(approx ( (+ (* x x) -1) (* x x)) (.f64 x x)) x x)) (/.f64 (.f64 x x) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 x x)) x x)))
(+.f64 (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x) x)
(+.f64 x (.f64 (neg.f64 (neg.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)))) x))
(+.f64 x (.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) x))
(.f64 #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) #s(approx ( (+ (* x x) -1) (* x x)) (*.f64 x x)))
#s(approx (* (+ (* x x) -1) (* x x)) (*.f64 x x))
(.f64 (.f64 #s(literal -1 binary64) x) x)
(.f64 #s(literal -1 binary64) (.f64 x x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal -1 binary64))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 x (.f64 #s(literal -1 binary64) x))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(neg.f64 (*.f64 x x))
(sqrt.f64 (pow.f64 x #s(literal 4 binary64)))
(fabs.f64 (*.f64 x x))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 x #s(literal 1 binary64))
(neg.f64 x)
(sqrt.f64 (*.f64 x x))
(fabs.f64 x)
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 x))
(+.f64 (cosh.f64 (log.f64 x)) (sinh.f64 (log.f64 x)))
x

eval17.0ms (0.3%)

Memory: 4.3MiB live, 48.9MiB allocated
Compiler: Compiled 7 180 to 510 computations (92.9% saved)

prune26.0ms (0.4%)

Memory

-33.5MiB live, 27.2MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	132	7	139

Accuracy

100.0%

Counts

139 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	64.1%	(/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -1 binary64)))
✓	77.6%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	27.3%	(/.f64 x #s(approx (+ (* x x) 1) (*.f64 x x)))
✓	52.8%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	52.8%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 (.f64 (fma.f64 x x #s(literal -1 binary64)) (.f64 x x)) x x))
✓	51.9%	#s(approx (/ x (+ (* x x) 1)) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (*.f64 (neg.f64 x) x)) x x))
✓	49.8%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 228 to 98 computations (57% saved)

regimes7.0ms (0.1%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

10 → 2

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.9%	2	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
100.0%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes3.0ms (0%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

7 → 2

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
100.0%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes34.0ms (0.6%)

Memory

-30.4MiB live, 16.5MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

2 calls:

32.0ms	x
2.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Results

Accuracy	Segments	Branch
79.4%	3	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
99.1%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes1.0ms (0%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
98.8%	2	`x`

Compiler

Compiled 1 to 1 computations (0% saved)

regimes2.0ms (0%)

Memory

6.6MiB live, 6.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
49.8%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
49.8%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch6.0ms (0.1%)

Memory

10.2MiB live, 10.2MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
5.0ms	12313368.166655952	6879933718.37258

Samples

2.0ms

64×

valid

Compiler

Compiled 114 to 77 computations (32.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

exact: 0.0ms (0% of total)

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

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
0.0ms	12313368.166655952	6879933718.37258

Compiler

Compiled 27 to 23 computations (14.8% saved)

bsearch30.0ms (0.5%)

Memory

-25.6MiB live, 19.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
29.0ms	0.013314840706471199	150.81022056384694

Samples

5.0ms

128×

valid

Compiler

Compiled 298 to 193 computations (35.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-div: 1.0ms (38.8% of total)

ival-add: 1.0ms (38.8% of total)

ival-mult: 1.0ms (38.8% of total)

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

exact: 0.0ms (0% of total)

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

bsearch4.0ms (0.1%)

Memory

6.1MiB live, 6.1MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
3.0ms	0.013314840706471199	150.81022056384694

Samples

1.0ms

32×

valid

Compiler

Compiled 170 to 145 computations (14.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

exact: 0.0ms (0% of total)

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

simplify93.0ms (1.6%)

Memory

3.3MiB live, 46.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	126
1	53	126
2	116	126
3	400	124
4	1554	124
5	4245	124
6	6138	124
7	7807	124

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 200000000 binary64)) (/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 20000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 (neg.f64 x) x)) x x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Outputs
(if (<=.f64 x #s(literal 200000000 binary64)) (/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 200000000 binary64)) (/.f64 (.f64 x (fma.f64 x x #s(literal -1 binary64))) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -1 binary64))) #s(approx (/ x (+ ( x x) 1)) (pow.f64 x #s(literal -1 binary64))))
(if (<=.f64 x #s(literal 20000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 20000000 binary64)) (/.f64 x (fma.f64 x x #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64))))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 (neg.f64 x) x)) x x)) #s(approx (/ x (+ ( x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 7746191359077253/9007199254740992 binary64)) #s(approx (/ x (+ (* x x) 1)) (fma.f64 #s(approx (* (+ (* x x) -1) (* x x)) (.f64 (neg.f64 x) x)) x x)) #s(approx (/ x (+ ( x x) 1)) (pow.f64 x #s(literal -1 binary64))))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x)))
(if (<=.f64 x #s(literal 1 binary64)) (/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64))) #s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64))))
#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))
#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))

soundness1.0s (17.3%)

Memory

33.7MiB live, 436.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	33	15
2	220	15
3	2396	15
0	9401	13
0	45	152
1	128	150
2	336	142
3	1106	140
4	2977	137
5	7066	135
0	8174	131
0	22	95
0	34	95
1	130	95
2	888	93
0	9606	93
0	65	308
1	173	298
2	411	298
3	1289	294
4	3369	286
5	7858	283
0	8580	278

Stop Event

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

Compiler

Compiled 229 to 104 computations (54.6% saved)

preprocess87.0ms (1.5%)

Memory: 21.1MiB live, 112.5MiB allocated
Compiler: Compiled 400 to 158 computations (60.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	7	17
1	24	15
2	56	14
3	71	14
4	91	14
0	5	7
0	8	7
1	15	7
2	34	7
3	61	7
4	78	7
5	81	7
6	89	7
7	91	7
0	91	6

Iter	Nodes	Cost
0	7	17
1	24	15
2	56	14
3	71	14
4	91	14
0	5	7
0	8	7
1	15	7
2	34	7
3	61	7
4	78	7
5	81	7
6	89	7
7	91	7
0	91	6

start0.0ms (0%)

analyze0.0ms (0%)

sample1.0s (17%)

explain96.0ms (1.6%)

preprocess17.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify5.0ms (0.1%)

localize20.0ms (0.3%)

series2.0ms (0%)

simplify141.0ms (2.4%)

rewrite222.0ms (3.8%)

eval30.0ms (0.5%)

prune8.0ms (0.1%)

simplify169.0ms (2.9%)

localize231.0ms (3.9%)

series6.0ms (0.1%)

simplify332.0ms (5.6%)

rewrite347.0ms (5.9%)

eval105.0ms (1.8%)

prune103.0ms (1.7%)

simplify300.0ms (5.1%)

localize71.0ms (1.2%)

series4.0ms (0.1%)

simplify168.0ms (2.9%)

rewrite212.0ms (3.6%)

eval170.0ms (2.9%)

prune26.0ms (0.4%)

simplify203.0ms (3.4%)

localize93.0ms (1.6%)

series3.0ms (0.1%)

simplify326.0ms (5.5%)

rewrite140.0ms (2.4%)

eval17.0ms (0.3%)

prune26.0ms (0.4%)

regimes7.0ms (0.1%)

regimes3.0ms (0%)

regimes34.0ms (0.6%)

regimes1.0ms (0%)

regimes2.0ms (0%)

bsearch6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch30.0ms (0.5%)

bsearch4.0ms (0.1%)

simplify93.0ms (1.6%)

soundness1.0s (17.3%)

preprocess87.0ms (1.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	7	17
1	24	15
2	56	14
3	71	14
4	91	14
0	5	7
0	8	7
1	15	7
2	34	7
3	61	7
4	78	7
5	81	7
6	89	7
7	91	7
0	91	6