Metrics for x / (x^2 + 1)

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

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)

sample932.0ms (30%)

Memory

35.6MiB live, 629.9MiB allocated; 955ms collecting garbage

Samples

701.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 275.0ms

ival-add: 125.0ms (45.4% of total)

ival-mult: 76.0ms (27.6% of total)

ival-div: 59.0ms (21.4% of total)

ival-true: 6.0ms (2.2% of total)

exact: 5.0ms (1.8% of total)

ival-assert: 3.0ms (1.1% of total)

adjust: 2.0ms (0.7% of total)

Bogosity

explain76.0ms (2.5%)

Memory

6.9MiB live, 96.0MiB allocated; 15ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
49	-	-	`(/.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	49	0
↳	`(*.f64 x x)`	overflow	49
↳	`(+.f64 (*.f64 x x) #s(literal 1 binary64))`	overflow	49

Confusion

	Predicted +	Predicted -
+	49	0
-	0	207

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	49	0	0
-	0	0	207

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	207
1	49

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

21.0ms

512×

valid

Compiler

Compiled 45 to 19 computations (57.8% saved)

Precisions

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

ival-mult: 4.0ms (36.3% of total)

ival-div: 3.0ms (27.3% of total)

ival-add: 2.0ms (18.2% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

preprocess37.0ms (1.2%)

Memory

-25.0MiB live, 20.4MiB allocated; 6ms collecting garbage

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; 0ms collecting garbage
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	82.0%	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

series3.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated; 0ms collecting garbage

Counts

5 → 15

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
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))
(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))))
(* -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 x) 1)) x (+ (* x x) 1) (* x x) 1)
1.0ms	x	@	-inf	((/ x (+ (* x x) 1)) x (+ (* x x) 1) (* x x) 1)
1.0ms	x	@	0	((/ x (+ (* x x) 1)) x (+ (* x x) 1) (* x x) 1)

simplify143.0ms (4.6%)

Memory

-3.4MiB live, 146.9MiB allocated; 43ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	152
1	128	150
2	336	142
3	1104	140
4	2985	137
5	7051	135
0	8161	131

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 14

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))
(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))))
(* -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
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))
(pow x 2)
(*.f64 x 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 (/.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))))
(fma.f64 x x #s(literal 1 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 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 3 binary64)) (/.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #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))

rewrite144.0ms (4.6%)

Memory

8.0MiB live, 151.2MiB allocated; 29ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	17
0	8	17
1	33	17
2	220	17
3	2396	17
0	9401	15

Stop Event

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

Counts

5 → 259

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

eval36.0ms (1.1%)

Memory: 27.8MiB live, 71.6MiB allocated; 8ms collecting garbage
Compiler: Compiled 7 231 to 977 computations (86.5% saved)

prune24.0ms (0.8%)

Memory

-31.0MiB live, 15.3MiB allocated; 3ms collecting garbage

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	312	4	316
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	313	4	317

Accuracy

100.0%

Counts

317 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.4%	(/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (+.f64 (.f64 x x) #s(literal 1 binary64)))
▶	82.0%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
▶	51.4%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
▶	51.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 37 to 26 computations (29.7% saved)

simplify0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

series4.0ms (0.1%)

Memory

5.6MiB live, 5.6MiB allocated; 0ms collecting garbage

Counts

13 → 22

Calls

Call 1

Inputs
#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)))
#s(approx (+ (* x x) 1) #s(literal 1 binary64))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(fma.f64 x x #s(literal 1 binary64))
(/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (+.f64 (.f64 x x) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(sqrt.f64 x)
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(*.f64 x 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 x)
1
(+ 1 (pow x 2))
(sqrt x)
(pow x 2)
(/ (- 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))))
(* -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 (sqrt -1) 2) x))
(* -1 (/ (+ (* -1 (/ (pow (sqrt -1) 2) (pow x 2))) (pow (sqrt -1) 2)) x))
(* -1 (/ (- (+ (/ (pow (sqrt -1) 2) (pow x 4)) (pow (sqrt -1) 2)) (/ (pow (sqrt -1) 2) (pow x 2))) x))
(* -1 (/ (- (+ (* -1 (/ (pow (sqrt -1) 2) (pow x 6))) (pow (sqrt -1) 2)) (+ (* -1 (/ (pow (sqrt -1) 2) (pow x 4))) (/ (pow (sqrt -1) 2) (pow x 2)))) x))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) (+ (* x x) 1) (* x x))
1.0ms	x	@	0	((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) (+ (* x x) 1) (* x x))
1.0ms	x	@	inf	((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) (+ (* x x) 1) (* x x))

Time

Variable

Point

Expression

2.0ms

-inf

((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) (+ (* x x) 1) (* x x))

1.0ms

((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) (+ (* x x) 1) (* x x))

1.0ms

inf

((/ x (+ (* x x) 1)) (/ 1 x) 1 x (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ x (+ (* x x) 1)) (+ (* x x) 1) (/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) (+ (* x x) 1) (* x x))

simplify74.0ms (2.4%)

Memory

5.1MiB live, 64.1MiB allocated; 7ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	202
1	209	200
2	648	192
0	2747	187

Stop Event

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

Counts

22 → 21

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

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

rewrite337.0ms (10.9%)

Memory

13.0MiB live, 200.6MiB allocated; 41ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	63
0	26	55
1	67	55
2	331	55
3	2525	55
0	8606	55

Stop Event

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

Counts

13 → 626

Calls

Call 1

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

Outputs
#s(approx (/ x (+ (* x x) 1)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (sqrt.f64 x) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal -2 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal -2 binary64)) (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal -2 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal -2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal -2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal -2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 x) #s(literal -1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 7/2 binary64)) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 7/4 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal -2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 x #s(literal -1 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -1 binary64)))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal -1/8 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal -4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -2 binary64))
(pow.f64 x #s(literal -1 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (log.f64 x)) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (neg.f64 (log.f64 x))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (log.f64 x)) (cosh.f64 (log.f64 x)) (-.f64 (.f64 (sinh.f64 (neg.f64 (log.f64 x))) (sinh.f64 (neg.f64 (log.f64 x)))) (.f64 (cosh.f64 (log.f64 x)) (sinh.f64 (neg.f64 (log.f64 x)))))))
(/.f64 (neg.f64 (pow.f64 x #s(literal -3/4 binary64))) (neg.f64 (pow.f64 x #s(literal 1/4 binary64))))
(/.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))
(/.f64 #s(literal -1 binary64) x)
(/.f64 #s(literal 1 binary64) x)
(neg.f64 (pow.f64 x #s(literal -1 binary64)))
(-.f64 (cosh.f64 (log.f64 x)) (sinh.f64 (log.f64 x)))
(fabs.f64 (pow.f64 x #s(literal -1 binary64)))
(exp.f64 (-.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (log.f64 (sqrt.f64 x))))
(exp.f64 (-.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)) (log.f64 (sqrt.f64 x))))
(exp.f64 (-.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64)) (log.f64 (sqrt.f64 x))))
(exp.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (neg.f64 (log.f64 (sqrt.f64 x)))))
(exp.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (+.f64 (neg.f64 (log.f64 (sqrt.f64 x))) (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/2 binary64) (neg.f64 (log.f64 (sqrt.f64 x)))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/2 binary64) (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 x) #s(literal -1/2 binary64) (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64) (neg.f64 (log.f64 (sqrt.f64 x)))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64) (*.f64 (log.f64 x) #s(literal -1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64) (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal -1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (neg.f64 (log.f64 (sqrt.f64 x))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 4 binary64) (log.f64 x)) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 x)) #s(literal -2 binary64)))
(exp.f64 (neg.f64 (log.f64 x)))
(+.f64 (cosh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))) (sinh.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(+.f64 (cosh.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal -2 binary64))) (sinh.f64 (.f64 (log.f64 (sqrt.f64 x)) #s(literal -2 binary64))))
(+.f64 (cosh.f64 (log.f64 x)) (sinh.f64 (neg.f64 (log.f64 x))))
#s(literal 1 binary64)
(*.f64 (sqrt.f64 (pow.f64 x #s(literal 7/4 binary64))) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) x)
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)) x)
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/8 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 2 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/8 binary64)) (pow.f64 (pow.f64 x #s(literal 5/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (sqrt.f64 (pow.f64 x #s(literal 7/4 binary64))))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 7/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/8 binary64)) (pow.f64 (pow.f64 x #s(literal 7/2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 2 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(*.f64 #s(literal 1 binary64) x)
(*.f64 x (sqrt.f64 #s(literal -1 binary64)))
(*.f64 x (pow.f64 #s(literal -1 binary64) #s(literal 1/2 binary64)))
(*.f64 x #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 (sqrt.f64 x)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (log.f64 x))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/8 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 2 binary64))
(pow.f64 x #s(literal 1 binary64))
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(neg.f64 x)
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(+.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 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 18 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (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 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 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 (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 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 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)))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
(*.f64 (pow.f64 (pow.f64 x #s(literal 7/4 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 1/8 binary64)) #s(literal 4 binary64)) (pow.f64 (pow.f64 x #s(literal 3/8 binary64)) #s(literal 4 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 4 binary64)) (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 4 binary64)))
(*.f64 (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 4 binary64)) x)
(*.f64 (pow.f64 x #s(literal 7/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (pow.f64 x #s(literal 5/4 binary64)) (pow.f64 x #s(literal 3/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/4 binary64)) (pow.f64 x #s(literal 5/4 binary64)))
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (sqrt.f64 x))
(.f64 (.f64 x x) #s(literal -1 binary64))
(.f64 (.f64 x x) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 x #s(literal 7/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 7/4 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x x))
(*.f64 (sqrt.f64 x) (pow.f64 x #s(literal 3/2 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x x))
(*.f64 x (pow.f64 (neg.f64 (pow.f64 x #s(literal 1/4 binary64))) #s(literal 4 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 4 binary64)) (log.f64 (sqrt.f64 x)))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.f64 x) #s(literal 2 binary64)))
(pow.f64 (pow.f64 x #s(literal 8 binary64)) #s(literal 1/4 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 8 binary64))
(pow.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 x #s(literal 2 binary64))
(/.f64 (+.f64 (pow.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64)) (pow.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) #s(literal 3 binary64))) (fma.f64 (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (cosh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (-.f64 (.f64 (sinh.f64 (.f64 (log.f64 x) #s(literal 2 binary64))) (sinh.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)))))))
(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 #s(literal 4 binary64) (log.f64 x)) #s(literal 1/2 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))))

eval118.0ms (3.8%)

Memory: -35.9MiB live, 207.5MiB allocated; 33ms collecting garbage
Compiler: Compiled 14 088 to 2 109 computations (85% saved)

prune32.0ms (1%)

Memory

-1.9MiB live, 45.5MiB allocated; 2ms collecting garbage

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	777	1	778
Fresh	0	0	0
Picked	1	3	4
Done	0	0	0
Total	778	4	782

Accuracy

100.0%

Counts

782 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	81.4%	(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (fma.f64 x x #s(literal 1 binary64)))
✓	82.0%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	51.4%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	51.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 36 to 25 computations (30.6% saved)

simplify0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

series2.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Counts

6 → 19

Calls

Call 1

Inputs
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (sqrt.f64 x) (sqrt.f64 x))
(sqrt.f64 x)
x
(fma.f64 x x #s(literal 1 binary64))
#s(literal 1 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))))
(sqrt x)
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)
(* (pow x 2) (+ 1 (/ 1 (pow x 2))))
(* -1 (/ (pow (sqrt -1) 2) x))
(* -1 (/ (+ (* -1 (/ (pow (sqrt -1) 2) (pow x 2))) (pow (sqrt -1) 2)) x))
(* -1 (/ (- (+ (/ (pow (sqrt -1) 2) (pow x 4)) (pow (sqrt -1) 2)) (/ (pow (sqrt -1) 2) (pow x 2))) x))
(* -1 (/ (- (+ (* -1 (/ (pow (sqrt -1) 2) (pow x 6))) (pow (sqrt -1) 2)) (+ (* -1 (/ (pow (sqrt -1) 2) (pow x 4))) (/ (pow (sqrt -1) 2) (pow x 2)))) x))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) x (+ (* x x) 1) 1)
1.0ms	x	@	inf	((/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) x (+ (* x x) 1) 1)
0.0ms	x	@	0	((/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) x (+ (* x x) 1) 1)

Time

Variable

Point

Expression

1.0ms

-inf

((/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) x (+ (* x x) 1) 1)

1.0ms

inf

((/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) x (+ (* x x) 1) 1)

0.0ms

((/ (* (sqrt x) (sqrt x)) (+ (* x x) 1)) (* (sqrt x) (sqrt x)) (sqrt x) x (+ (* x x) 1) 1)

simplify132.0ms (4.3%)

Memory

8.6MiB live, 53.7MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	157
1	180	155
2	570	147
0	2365	142

Stop Event

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

Counts

19 → 18

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

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

rewrite145.0ms (4.7%)

Memory

23.4MiB live, 74.7MiB allocated; 9ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	11	15
1	48	15
2	278	15
3	2344	15
0	8269	15

Stop Event

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

Counts

6 → 326

Calls

Call 1

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

Outputs
(*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) x)) (-.f64 x #s(literal 1 binary64)))
(.f64 (.f64 (/.f64 (sqrt.f64 x) (fma.f64 x x #s(literal -1 binary64))) (pow.f64 x #s(literal 1/4 binary64))) (pow.f64 x #s(literal 1/4 binary64)))
(.f64 (/.f64 (sqrt.f64 x) (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))) (.f64 (fma.f64 x x #s(literal -1 binary64)) (sqrt.f64 x)))
(.f64 (/.f64 (sqrt.f64 x) (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (sqrt.f64 x)))
(*.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 4 binary64)) #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64)))
(*.f64 (/.f64 x (+.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 x (+.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 (pow.f64 x #s(literal 1/4 binary64)) (.f64 (pow.f64 x #s(literal 1/4 binary64)) (/.f64 (sqrt.f64 x) (fma.f64 x x #s(literal -1 binary64)))))
(*.f64 (/.f64 (sqrt.f64 x) (fma.f64 x x #s(literal -1 binary64))) (sqrt.f64 x))
(*.f64 (fma.f64 x x #s(literal -1 binary64)) (/.f64 x (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 1 binary64))))
(*.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))))
(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (fma.f64 x x #s(literal -1 binary64))))
(/.f64 (+.f64 (pow.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal 3 binary64)) (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal 3 binary64))) (fma.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (-.f64 (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))))) (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))))))))
(/.f64 (+.f64 (pow.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal 3 binary64)) (pow.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) #s(literal 3 binary64))) (fma.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (-.f64 (.f64 (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))))) (.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 (fma.f64 x x #s(literal 1 binary64)) (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))))))))
(/.f64 (+.f64 (pow.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x x #s(literal 1 binary64))) #s(literal 3 binary64)) (pow.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))) #s(literal 3 binary64))) (fma.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x x #s(literal 1 binary64))) (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x x #s(literal 1 binary64))) (-.f64 (.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64)))) (.f64 (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 x x #s(literal 1 binary64))) (.f64 (/.f64 x (+.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 x #s(literal 4 binary64)))))))
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(-.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 (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 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (+.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 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)))
(-.f64 #s(literal 1 binary64) (*.f64 x x))
(+.f64 (/.f64 (/.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 (/.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 -2 binary64)) (.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)))) (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 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -3 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 -2 binary64)) (.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)))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 binary64)))))))
(+.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 1 binary64)) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal 2 binary64))))
(+.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 #s(literal 1 binary64) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 (/.f64 #s(literal 1 binary64) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 (pow.f64 x #s(literal 18 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 (/.f64 (*.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 1 binary64))) (fma.f64 x x #s(literal 1 binary64))) (/.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 binary64))))
(+.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 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 18 binary64)) (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #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 (pow.f64 (-.f64 (+.f64 (pow.f64 x #s(literal 12 binary64)) #s(literal 1 binary64)) (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 (/.f64 (fma.f64 x x #s(literal -1 binary64)) (fma.f64 x x #s(literal -1 binary64))) (/.f64 (fma.f64 x x (pow.f64 x #s(literal 4 binary64))) (fma.f64 x x #s(literal 1 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 (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 x #s(literal 6 binary64)) (+.f64 (fma.f64 x x #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (fma.f64 x (-.f64 (pow.f64 x #s(literal 3 binary64)) x) #s(literal 1 binary64)) #s(literal -1 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)))
(+.f64 (*.f64 x x) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 x x))
#s(literal 1 binary64)

eval198.0ms (6.4%)

Memory: 10.1MiB live, 97.4MiB allocated; 10ms collecting garbage
Compiler: Compiled 8 030 to 1 102 computations (86.3% saved)

prune10.0ms (0.3%)

Memory

-19.1MiB live, 22.5MiB allocated; 8ms collecting garbage

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	347	0	347
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	347	4	351

Accuracy

100.0%

Counts

351 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	81.4%	(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (fma.f64 x x #s(literal 1 binary64)))
✓	82.0%	(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
✓	51.4%	(/.f64 x #s(approx (+ (* x x) 1) #s(literal 1 binary64)))
✓	51.0%	#s(approx (/ x (+ (* x x) 1)) (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 90 to 44 computations (51.1% saved)

regimes5.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB allocated; 0ms collecting garbage

Counts

6 → 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)))
(/.f64 x (fma.f64 x x #s(literal 1 binary64)))
(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
(/.f64 (*.f64 (sqrt.f64 x) (sqrt.f64 x)) (fma.f64 x x #s(literal 1 binary64)))
(/.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (+.f64 (.f64 x x) #s(literal 1 binary64)))

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

Calls

2 calls:

2.0ms	x
2.0ms	(/.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 (0.1%)

Memory

9.2MiB live, 9.2MiB allocated; 0ms collecting garbage

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

2 calls:

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

Results

Accuracy	Segments	Branch
77.3%	4	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
98.4%	2	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

regimes27.0ms (0.9%)

Memory

-36.0MiB live, 17.2MiB allocated; 16ms collecting garbage

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:

25.0ms	(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))
1.0ms	x

Results

Accuracy	Segments	Branch
51.0%	1	`(/.f64 x (+.f64 (*.f64 x x) #s(literal 1 binary64)))`
51.0%	1	`x`

Compiler

Compiled 8 to 6 computations (25% saved)

bsearch2.0ms (0.1%)

Memory

4.8MiB live, 4.8MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	predicate-same

Steps

Time	Left	Right
2.0ms	3761449.599112383	1148095910610.6707

Samples

1.0ms

16×

valid

Compiler

Compiled 27 to 23 computations (14.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 0.0ms

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

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

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

adjust: 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)

bsearch11.0ms (0.3%)

Memory

23.3MiB live, 23.3MiB allocated; 0ms collecting garbage

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
9.0ms	0.005940710304197364	1.205741275307742

Samples

5.0ms

112×

valid

Compiler

Compiled 150 to 128 computations (14.7% saved)

Precisions

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

ival-div: 1.0ms (39.7% of total)

ival-add: 1.0ms (39.7% of total)

ival-mult: 1.0ms (39.7% of total)

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

adjust: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

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

simplify20.0ms (0.6%)

Memory

-3.7MiB live, 36.1MiB allocated; 13ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	56
1	25	56
2	44	56
3	71	56
4	88	56
5	91	56
6	98	56
7	106	56
8	110	56

Stop Event

1×

saturated

Calls

Call 1

Inputs

(if (<=.f64 x #s(literal 5000000 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 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 5000000 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 5000000 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 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)))

derivations347.0ms (11.2%)

Memory

-0.1MiB live, 271.3MiB allocated; 47ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	152
1	128	150
2	336	142
3	1104	140
4	2985	137
5	7051	135
0	8161	131
0	5	17
0	8	17
1	33	17
2	220	17
3	2396	17
0	9401	15

Stop Event

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

Compiler

Compiled 56 to 18 computations (67.9% saved)

preprocess240.0ms (7.7%)

Memory: -15.2MiB live, 191.5MiB allocated; 38ms collecting garbage
Compiler: Compiled 224 to 112 computations (50% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

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%)

analyze1.0ms (0%)

sample932.0ms (30%)

explain76.0ms (2.5%)

preprocess37.0ms (1.2%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify0.0ms (0%)

series3.0ms (0.1%)

simplify143.0ms (4.6%)

rewrite144.0ms (4.6%)

eval36.0ms (1.1%)

prune24.0ms (0.8%)

simplify0.0ms (0%)

series4.0ms (0.1%)

simplify74.0ms (2.4%)

rewrite337.0ms (10.9%)

eval118.0ms (3.8%)

prune32.0ms (1%)

simplify0.0ms (0%)

series2.0ms (0.1%)

simplify132.0ms (4.3%)

rewrite145.0ms (4.7%)

eval198.0ms (6.4%)

prune10.0ms (0.3%)

regimes5.0ms (0.1%)

regimes3.0ms (0.1%)

regimes27.0ms (0.9%)

bsearch2.0ms (0.1%)

bsearch11.0ms (0.3%)

simplify20.0ms (0.6%)

derivations347.0ms (11.2%)

preprocess240.0ms (7.7%)

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