Metrics for Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, H

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample784.0ms (18.2%)

Memory

11.7MiB live, 845.2MiB allocated

Samples

449.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 179.0ms

ival-mult: 67.0ms (37.5% of total)

ival-div: 55.0ms (30.8% of total)

ival-sub: 39.0ms (21.8% of total)

exact: 8.0ms (4.5% of total)

ival-true: 6.0ms (3.4% of total)

ival-assert: 3.0ms (1.7% of total)

Bogosity

explain65.0ms (1.5%)

Memory

9.0MiB live, 121.3MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 6 binary64)`
-	-	`#s(literal 3 binary64)`
-	-	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
-	-	`(*.f64 x x)`
-	-	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

22.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

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

ival-mult: 4.0ms (37.3% of total)

ival-div: 3.0ms (28% of total)

ival-sub: 2.0ms (18.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess26.0ms (0.6%)

Memory

-1.3MiB live, 39.4MiB allocated

Algorithm

1×	egg-herbie

Rules

40×	`associate-/l*`
36×	`distribute-lft-neg-in`
36×	`associate-r`
32×	`sub-neg`
30×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	31	14
2	69	14
3	166	14
4	292	14
5	371	14
6	397	14
7	405	14
0	6	7
0	9	7
1	16	7
2	22	7
3	24	7
0	24	6

Stop Event

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

Calls

Call 1

Inputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))

Outputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(/.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 6 binary64))

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
cost-diff	128	(-.f64 (*.f64 x x) #s(literal 3 binary64))

Rules

8×	`lower-+.f64`
8×	`lower-+.f32`
6×	`lower-fma.f64`
6×	`lower-/.f32`
6×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
0	9	18
1	16	18
2	22	18
3	24	18
0	24	16

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(-.f64 (*.f64 x x) #s(literal 3 binary64))
(*.f64 x x)
x
#s(literal 3 binary64)
#s(literal 6 binary64)

Outputs
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(/.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 6 binary64))
(-.f64 (*.f64 x x) #s(literal 3 binary64))
(fma.f64 x x #s(literal -3 binary64))
(*.f64 x x)
x
#s(literal 3 binary64)
#s(literal 6 binary64)

localize69.0ms (1.6%)

Memory

0.6MiB live, 36.3MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 (*.f64 x x) #s(literal 3 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.07421875	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))

Samples

65.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-mult: 55.0ms (93.6% of total)

ival-div: 2.0ms (3.4% of total)

ival-sub: 1.0ms (1.7% 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

8.2MiB live, 8.2MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())

Inputs

#s(alt (-.f64 (*.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (*.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())

#s(alt (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())

#s(alt (*.f64 x x) (patch (*.f64 x x) #<representation binary64>) () ())

Outputs
#s(alt -3 (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (pow x 2) 3) (taylor 0 x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (-.f64 (.f64 x x) #s(literal 3 binary64)) (patch (-.f64 (.f64 x x) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) (patch (/.f64 (-.f64 (.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	((- (* x x) 3) (/ (- (* x x) 3) 6) (* x x))
1.0ms	x	@	0	((- (* x x) 3) (/ (- (* x x) 3) 6) (* x x))
0.0ms	x	@	-inf	((- (* x x) 3) (/ (- (* x x) 3) 6) (* x x))

simplify155.0ms (3.6%)

Memory

15.3MiB live, 91.9MiB allocated

Algorithm

1×	egg-herbie

Rules

4 388×	`lower-*.f64`
4 388×	`lower-*.f32`
2 828×	`lower-fma.f64`
2 828×	`lower-fma.f32`
1 846×	`cube-prod`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	162
1	43	162
2	98	162
3	236	162
4	759	162
5	1590	162
6	2334	162
7	3514	162
8	4236	162
9	5345	162
10	6402	162
11	7126	162
0	8039	144

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

rewrite208.0ms (4.8%)

Memory

-47.9MiB live, 224.8MiB allocated

Rules

5 168×	`lower-/.f32`
5 166×	`lower-/.f64`
4 318×	`lower-*.f32`
4 316×	`lower-*.f64`
4 062×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	15
0	9	15
1	42	15
2	230	15
3	1831	15
0	8685	13

Stop Event

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

Counts

3 → 516

Calls

Call 1

Inputs
(-.f64 (*.f64 x x) #s(literal 3 binary64))
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(*.f64 x x)

Outputs
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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eval99.0ms (2.3%)

Memory: 22.8MiB live, 136.2MiB allocated
Compiler: Compiled 14 583 to 1 649 computations (88.7% saved)

prune16.0ms (0.4%)

Memory

-26.7MiB live, 45.7MiB allocated

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	544	8	552
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	545	8	553

Accuracy

100.0%

Counts

553 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
▶	99.8%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
▶	99.8%	(fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
	66.4%	(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64)))
▶	47.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	99.9%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
	47.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
▶	52.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 108 to 96 computations (11.1% saved)

simplify5.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 x #s(literal -2 binary64))
cost-diff	0	(pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))
cost-diff	5952	(fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (* x x) 3) (*.f64 x x))
cost-diff	0	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
cost-diff	0	(*.f64 x #s(literal 1/6 binary64))
cost-diff	0	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
cost-diff	0	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 x x #s(literal -3 binary64))
cost-diff	0	(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
cost-diff	1088	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))

Rules

26×	`lower-*.f32`
22×	`lower-*.f64`
18×	`lower-fma.f32`
16×	`lower-+.f64`
16×	`lower-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	90
0	36	85
1	56	84
2	72	84
3	74	84
0	74	84

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
#s(literal 6 binary64)
(fma.f64 x x #s(literal -3 binary64))
x
#s(literal -3 binary64)
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(literal -1/2 binary64)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/6 binary64))
x
#s(literal 1/6 binary64)
#s(literal -1/2 binary64)
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
#s(approx (- (* x x) 3) (*.f64 x x))
(*.f64 x x)
x
#s(literal 6 binary64)
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
#s(literal 1/6 binary64)
(pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 x #s(literal -2 binary64))
x
#s(literal -2 binary64)
#s(literal -1 binary64)
#s(literal -1/2 binary64)

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

localize94.0ms (2.2%)

Memory

-2.0MiB live, 119.7MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 x #s(literal -2 binary64))
accuracy	0.09375	(fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
accuracy	0.37264757212343663	(pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.07421875	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
accuracy	33.52916937278251	#s(approx (- (* x x) 3) (*.f64 x x))
accuracy	0.04296875	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
accuracy	0.35546875	(*.f64 x #s(literal 1/6 binary64))
accuracy	30.592649701826353	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
accuracy	0	(fma.f64 x x #s(literal -3 binary64))
accuracy	0.0625	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
accuracy	0.345749626792152	(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))

Samples

62.0ms

256×

valid

Compiler

Compiled 87 to 24 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 49.0ms

ival-add: 25.0ms (50.6% of total)

ival-div: 7.0ms (14.2% of total)

ival-mult: 6.0ms (12.1% of total)

ival-pow: 5.0ms (10.1% of total)

const: 3.0ms (6.1% of total)

ival-sub: 1.0ms (2% of total)

exact: 1.0ms (2% of total)

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

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

series7.0ms (0.2%)

Memory

26.5MiB live, 26.5MiB allocated

Counts

12 → 144

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())
#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (- (* x x) 3) (.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())
#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())

Outputs
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* -2/3 (pow x 2)) 2) (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2) (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2) (taylor 0 x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt -3 (taylor 0 x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) (patch (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (/ 6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) (patch (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 x x #s(literal -3 binary64)) (patch (fma.f64 x x #s(literal -3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) (patch #s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (.f64 x #s(literal 1/6 binary64)) (patch (.f64 x #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (- (* x x) 3) (.f64 x x)) #s(literal 6 binary64)) (patch (/.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (patch (fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) (patch (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 1 (pow x 2)) (taylor -inf x) (#s(alt (pow.f64 x #s(literal -2 binary64)) (patch (pow.f64 x #s(literal -2 binary64)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify207.0ms (4.8%)

Memory

-14.2MiB live, 146.3MiB allocated

Algorithm

1×	egg-herbie

Rules

6 490×	`lower-fma.f64`
6 490×	`lower-fma.f32`
3 366×	`lower-*.f64`
3 366×	`lower-*.f32`
1 410×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	794
1	115	794
2	245	794
3	512	794
4	1279	794
5	2305	794
6	3205	794
7	4714	794
8	6053	794
9	7954	794
0	8085	725

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

Inputs
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-2
(- (* -2/3 (pow x 2)) 2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
-3
(- (pow x 2) 3)
(- (pow x 2) 3)
(- (pow x 2) 3)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-3
(- (pow x 2) 3)
(- (pow x 2) 3)
(- (pow x 2) 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
(- (* -2/3 (pow x 2)) 2)
(fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(fma.f64 (fma.f64 #s(literal -2/9 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -2/27 binary64) (.f64 x x) #s(literal -2/9 binary64)) (.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal -2 binary64))
-3
#s(literal -3 binary64)
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
-3
#s(literal -3 binary64)
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
(/ 1 (pow x 2))
(/.f64 #s(literal 1 binary64) (*.f64 x x))

rewrite434.0ms (10.1%)

Memory

10.3MiB live, 210.2MiB allocated

Rules

4 434×	`lower-fma.f32`
4 428×	`lower-fma.f64`
3 584×	`lower-*.f32`
3 580×	`lower-*.f64`
2 398×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	75
0	36	66
1	148	66
2	841	66
3	6272	66
0	8428	66

Stop Event

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

Counts

12 → 936

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
(/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))
(fma.f64 x x #s(literal -3 binary64))
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(*.f64 x #s(literal 1/6 binary64))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
#s(approx (- (* x x) 3) (*.f64 x x))
(*.f64 x x)
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64))
(pow.f64 x #s(literal -2 binary64))

Outputs
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eval137.0ms (3.2%)

Memory: -2.9MiB live, 233.8MiB allocated
Compiler: Compiled 17 455 to 1 578 computations (91% saved)

prune22.0ms (0.5%)

Memory

7.3MiB live, 82.9MiB allocated

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	1 077	3	1 080
Fresh	2	1	3
Picked	2	3	5
Done	0	0	0
Total	1 081	7	1 088

Accuracy

100.0%

Counts

1 088 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
▶	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	99.8%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	47.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	48.0%	(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)))
▶	47.5%	(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
✓	52.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 46 to 39 computations (15.2% saved)

simplify5.0ms (0.1%)

Memory

7.4MiB live, 7.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 x #s(literal 6 binary64))
cost-diff	0	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
cost-diff	0	(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
cost-diff	0	(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
cost-diff	0	#s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)))
cost-diff	0	(*.f64 x x)
cost-diff	0	#s(approx (- (* x x) 3) (*.f64 x x))
cost-diff	0	(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))

Rules

22×	`lower-*.f32`
20×	`lower-/.f32`
18×	`lower-*.f64`
16×	`lower-+.f32`
14×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	128
0	37	128
1	54	128
2	57	128
0	57	124

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
#s(approx (- (* x x) 3) (*.f64 x x))
(*.f64 x x)
x
#s(literal 1/6 binary64)
(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)))
#s(literal 1 binary64)
#s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
#s(literal 18 binary64)
(*.f64 x x)
x
#s(literal 6 binary64)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(*.f64 x x)
x
#s(literal 1/6 binary64)
#s(literal -1/2 binary64)
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 x #s(literal 6 binary64))
x
#s(literal 6 binary64)
#s(literal -1/2 binary64)

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

localize56.0ms (1.3%)

Memory

-21.4MiB live, 102.3MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x #s(literal 6 binary64))
accuracy	0.04296875	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.09375	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
accuracy	0.0625	(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)))
accuracy	0.11328125	(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
accuracy	0.5028368015508655	(/.f64 #s(literal 18 binary64) (*.f64 x x))
accuracy	33.92676128925058	#s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))
accuracy	0	(*.f64 x x)
accuracy	0.10546875	(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
accuracy	33.52916937278251	#s(approx (- (* x x) 3) (*.f64 x x))

Samples

42.0ms

256×

valid

Compiler

Compiled 100 to 25 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

ival-div: 11.0ms (37.1% of total)

ival-mult: 6.0ms (20.2% of total)

ival-add: 5.0ms (16.9% of total)

const: 5.0ms (16.9% of total)

ival-sub: 1.0ms (3.4% of total)

exact: 1.0ms (3.4% of total)

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

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

series8.0ms (0.2%)

Memory

18.6MiB live, 18.6MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#s(alt (.f64 #s(approx (- ( x x) 3) (.f64 x x)) #s(literal 1/6 binary64)) (patch (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #<representation binary64>) () ())
#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())
#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x)) (patch #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)) #<representation binary64>) () ())
#s(alt (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) (patch (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) (patch (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())

Outputs
#s(alt -1/2 (taylor 0 x) (#s(alt (.f64 #s(approx (- ( x x) 3) (.f64 x x)) #s(literal 1/6 binary64)) (patch (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (.f64 #s(approx (- ( x x) 3) (.f64 x x)) #s(literal 1/6 binary64)) (patch (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(approx (- ( x x) 3) (.f64 x x)) #s(literal 1/6 binary64)) (patch (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(approx (- ( x x) 3) (.f64 x x)) #s(literal 1/6 binary64)) (patch (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (.f64 #s(approx (- ( x x) 3) (.f64 x x)) #s(literal 1/6 binary64)) (patch (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 1/6 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (- (* x x) 3) (.f64 x x)) (patch #s(approx (- ( x x) 3) (*.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))) #<representation binary64>) () ())) ())
#s(alt (/ 6 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x)) (patch #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x)) (patch #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x)) (patch #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x)) (patch #s(approx (/ 6 (+ ( x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)) #<representation binary64>) () ())) ())
#s(alt (/ 6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) (patch (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) (patch (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) (patch (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) (patch (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) x) #<representation binary64>) () ())) ())
#s(alt (/ 6 x) (taylor -inf x) (#s(alt (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) (patch (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) (patch (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) (patch (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) (patch (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64)) x) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) (patch (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) (patch (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 x) (taylor -inf x) (#s(alt (/.f64 x #s(literal 6 binary64)) (patch (/.f64 x #s(literal 6 binary64)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 18 binary64) (.f64 x x)) (patch (/.f64 #s(literal 18 binary64) (.f64 x x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

((* (- (* x x) 3) 1/6) (- (* x x) 3) (* x x) (/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (/ (/ (+ (/ 18 (* x x)) 6) x) x) (/ (+ (/ 18 (* x x)) 6) x) (+ (* (* x x) 1/6) -1/2) (+ (* (/ x 6) x) -1/2) (/ x 6) (/ 18 (* x x)))

1.0ms

inf

((* (- (* x x) 3) 1/6) (- (* x x) 3) (* x x) (/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (/ (/ (+ (/ 18 (* x x)) 6) x) x) (/ (+ (/ 18 (* x x)) 6) x) (+ (* (* x x) 1/6) -1/2) (+ (* (/ x 6) x) -1/2) (/ x 6) (/ 18 (* x x)))

1.0ms

-inf

((* (- (* x x) 3) 1/6) (- (* x x) 3) (* x x) (/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (/ (/ (+ (/ 18 (* x x)) 6) x) x) (/ (+ (/ 18 (* x x)) 6) x) (+ (* (* x x) 1/6) -1/2) (+ (* (/ x 6) x) -1/2) (/ x 6) (/ 18 (* x x)))

simplify161.0ms (3.7%)

Memory

-7.8MiB live, 112.8MiB allocated

Algorithm

1×	egg-herbie

Rules

6 004×	`lower-fma.f64`
6 004×	`lower-fma.f32`
3 202×	`lower-*.f64`
3 202×	`lower-*.f32`
1 758×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	69	844
1	128	844
2	267	844
3	540	844
4	1333	844
5	2384	844
6	3321	844
7	4905	844
8	6155	844
0	8112	787

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-3
(- (pow x 2) 3)
(- (pow x 2) 3)
(- (pow x 2) 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-2
(- (* -2/3 (pow x 2)) 2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
(/ 18 (pow x 4))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/ 18 (pow x 3))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ 6 x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ 6 x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(/ 18 (pow x 2))
(/ 18 (pow x 2))

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
-3
#s(literal -3 binary64)
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
(- (* -2/3 (pow x 2)) 2)
(fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(fma.f64 (fma.f64 #s(literal -2/9 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
(fma.f64 (fma.f64 (fma.f64 #s(literal -2/27 binary64) (.f64 x x) #s(literal -2/9 binary64)) (.f64 x x) #s(literal -2/3 binary64)) (*.f64 x x) #s(literal -2 binary64))
(/ 18 (pow x 4))
(/.f64 #s(literal 18 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ 18 (pow x 3))
(/.f64 #s(literal 18 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 3 binary64)))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ 6 x)
(/.f64 #s(literal 6 binary64) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(fma.f64 x x #s(literal -3 binary64))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ 6 x)
(/.f64 #s(literal 6 binary64) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(* 1/6 x)
(*.f64 x #s(literal 1/6 binary64))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))
(/ 18 (pow x 2))
(/.f64 #s(literal 18 binary64) (*.f64 x x))

rewrite329.0ms (7.7%)

Memory

18.1MiB live, 126.5MiB allocated

Rules

5 260×	`lower-fma.f32`
5 256×	`lower-fma.f64`
4 920×	`lower-*.f32`
4 916×	`lower-*.f64`
4 088×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	103
0	37	103
1	160	103
2	925	103
0	8610	95

Stop Event

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

Counts

11 → 553

Calls

Call 1

Inputs
(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
#s(approx (- (* x x) 3) (*.f64 x x))
(*.f64 x x)
(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)))
#s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 x #s(literal 6 binary64))
(/.f64 #s(literal 18 binary64) (*.f64 x x))

Outputs
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eval339.0ms (7.9%)

Memory: -24.8MiB live, 176.2MiB allocated
Compiler: Compiled 12 161 to 1 853 computations (84.8% saved)

prune20.0ms (0.5%)

Memory

-4.6MiB live, 70.0MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	738	1	739
Fresh	0	0	0
Picked	1	3	4
Done	0	3	3
Total	739	7	746

Accuracy

100.0%

Counts

746 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	99.8%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	47.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	47.5%	(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))
✓	47.5%	(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
✓	52.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 41 to 36 computations (12.2% saved)

simplify4.0ms (0.1%)

Memory

13.5MiB live, 13.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	#s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x))
cost-diff	0	(/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)
cost-diff	0	#s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))
cost-diff	0	(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))

Rules

16×	`lower-/.f32`
10×	`lower-/.f64`
8×	`lower-+.f64`
8×	`lower-+.f32`
6×	`lift-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	82
0	19	82
1	25	82
0	25	80

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))
#s(literal 1 binary64)
#s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))
(/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)
#s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x))
(/.f64 #s(literal 6 binary64) x)
#s(literal 6 binary64)
x

Outputs
(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))
#s(literal 1 binary64)
#s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))
(/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)
#s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x))
(/.f64 #s(literal 6 binary64) x)
#s(literal 6 binary64)
x

localize31.0ms (0.7%)

Memory

-2.8MiB live, 84.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0625	(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))
accuracy	0.11328125	(/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)
accuracy	32.25042102137163	#s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x))
accuracy	33.92676128925058	#s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))

Samples

20.0ms

256×

valid

Compiler

Compiled 44 to 16 computations (63.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-div: 9.0ms (65.2% of total)

ival-add: 2.0ms (14.5% of total)

ival-mult: 2.0ms (14.5% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated

Counts

4 → 48

Calls

Call 1

Inputs
#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())
#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())

Outputs
#s(alt -1/2 (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (- (* 1/6 (pow x 2)) 1/2) (taylor 0 x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt -2 (taylor 0 x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (- (* -2/3 (pow x 2)) 2) (taylor 0 x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2) (taylor 0 x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2) (taylor 0 x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 4)) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 18 (* 6 (pow x 2))) (pow x 4)) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 18 (* 6 (pow x 2))) (pow x 4)) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 18 (* 6 (pow x 2))) (pow x 4)) (taylor 0 x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ 18 (pow x 3)) (taylor 0 x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 18 (* 6 (pow x 2))) (pow x 3)) (taylor 0 x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 18 (* 6 (pow x 2))) (pow x 3)) (taylor 0 x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 18 (* 6 (pow x 2))) (pow x 3)) (taylor 0 x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (/ 6 (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2)) (taylor inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 6 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ 6 x) (taylor inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (* 1/6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) (patch (/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))) #<representation binary64>) () ())) ())
#s(alt (/ 6 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) (patch #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)) #<representation binary64>) () ())) ())
#s(alt (/ 6 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) (patch (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x) #<representation binary64>) () ())) ())
#s(alt (/ 6 x) (taylor -inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())
#s(alt (/ (+ 6 (* 18 (/ 1 (pow x 2)))) x) (taylor -inf x) (#s(alt #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) (patch #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) #<representation binary64>) () ())) ())

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

((/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (/ (/ (+ (/ 18 (* x x)) 6) x) x) (/ (+ (/ 18 (* x x)) 6) x))

1.0ms

-inf

((/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (/ (/ (+ (/ 18 (* x x)) 6) x) x) (/ (+ (/ 18 (* x x)) 6) x))

1.0ms

inf

((/ 1 (/ 6 (+ (* x x) -3))) (/ 6 (+ (* x x) -3)) (/ (/ (+ (/ 18 (* x x)) 6) x) x) (/ (+ (/ 18 (* x x)) 6) x))

simplify149.0ms (3.5%)

Memory

-18.1MiB live, 143.7MiB allocated

Algorithm

1×	egg-herbie

Rules

6 958×	`lower-fma.f64`
6 958×	`lower-fma.f32`
3 578×	`lower-*.f64`
3 578×	`lower-*.f32`
1 398×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	438
1	111	438
2	228	438
3	442	438
4	867	438
5	1343	438
6	2113	438
7	3527	438
8	5100	438
9	6702	438
0	8138	417

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
-2
(- (* -2/3 (pow x 2)) 2)
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
(/ 18 (pow x 4))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/ 18 (pow x 3))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ 6 x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(* 1/6 (pow x 2))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/ 6 (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/ 6 x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)

Outputs
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
-2
#s(literal -2 binary64)
(- (* -2/3 (pow x 2)) 2)
(fma.f64 #s(literal -2/3 binary64) (*.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* -2/9 (pow x 2)) 2/3)) 2)
(fma.f64 (fma.f64 #s(literal -2/9 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -2 binary64))
(- (* (pow x 2) (- (* (pow x 2) (- (* -2/27 (pow x 2)) 2/9)) 2/3)) 2)
(fma.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -2/27 binary64) (fma.f64 (fma.f64 #s(literal -2/9 binary64) (.f64 x x) #s(literal -2/3 binary64)) (.f64 x x) #s(literal -2 binary64)))
(/ 18 (pow x 4))
(/.f64 #s(literal 18 binary64) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 4))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 4 binary64)))
(/ 18 (pow x 3))
(/.f64 #s(literal 18 binary64) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 3 binary64)))
(/ (+ 18 (* 6 (pow x 2))) (pow x 3))
(/.f64 (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64)) (pow.f64 x #s(literal 3 binary64)))
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ 6 x)
(/.f64 #s(literal 6 binary64) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(* 1/6 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (/ 54 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (.f64 x x))
(/ (+ 6 (+ (* 18 (/ 1 (pow x 2))) (+ (* 162 (/ 1 (pow x 6))) (/ 54 (pow x 4))))) (pow x 2))
(/.f64 (+.f64 (+.f64 (/.f64 #s(literal 162 binary64) (pow.f64 x #s(literal 6 binary64))) (+.f64 (/.f64 #s(literal 18 binary64) (.f64 x x)) #s(literal 6 binary64))) (/.f64 #s(literal 54 binary64) (pow.f64 x #s(literal 4 binary64)))) (.f64 x x))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)
(/ 6 x)
(/.f64 #s(literal 6 binary64) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)
(/ (+ 6 (* 18 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x)

rewrite127.0ms (3%)

Memory

-5.0MiB live, 191.2MiB allocated

Rules

3 902×	`lower-*.f64`
3 902×	`lower-*.f32`
2 974×	`lower-fma.f64`
2 974×	`lower-fma.f32`
2 888×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	76
0	19	76
1	96	76
2	607	76
3	5863	76
0	8143	70

Stop Event

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

Counts

4 → 72

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))
#s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x))
(/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)
#s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x))

Outputs
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eval15.0ms (0.3%)

Memory: -1.5MiB live, 37.0MiB allocated
Compiler: Compiled 1 465 to 283 computations (80.7% saved)

prune6.0ms (0.1%)

Memory

20.3MiB live, 20.4MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	120	7	127

Accuracy

100.0%

Counts

127 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	99.8%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	47.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	47.5%	(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))
✓	47.5%	(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
✓	52.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 137 to 84 computations (38.7% saved)

regimes17.0ms (0.4%)

Memory

5.0MiB live, 43.7MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64))))
(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 #s(approx (/ (+ (/ 18 (* x x)) 6) x) (/.f64 #s(literal 6 binary64) x)) x)))
(/.f64 #s(literal 1 binary64) #s(approx (/ 6 (+ (* x x) -3)) (/.f64 (/.f64 (+.f64 (/.f64 #s(literal 18 binary64) (*.f64 x x)) #s(literal 6 binary64)) x) x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64)))
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (pow.f64 x #s(literal -2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))

Outputs
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))

Calls

4 calls:

5.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))
4.0ms	x
4.0ms	(*.f64 x x)
4.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
99.9%	1	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
99.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes11.0ms (0.3%)

Memory

-16.7MiB live, 27.2MiB allocated

Counts

6 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))

Outputs
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))

Calls

4 calls:

4.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
3.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
99.9%	1	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
99.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes8.0ms (0.2%)

Memory

23.4MiB live, 23.4MiB allocated

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))

Outputs
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))

Calls

4 calls:

2.0ms	x
2.0ms	(*.f64 x x)
2.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
2.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))

Results

Accuracy	Segments	Branch
99.8%	1	`x`
99.8%	1	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
99.8%	1	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
99.8%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes7.0ms (0.2%)

Memory

-17.9MiB live, 21.3MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))

Outputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))

Calls

4 calls:

2.0ms	(*.f64 x x)
2.0ms	x
1.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
1.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))

Results

Accuracy	Segments	Branch
97.8%	2	`x`
97.8%	2	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
97.8%	2	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
97.8%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.1%)

Memory

11.2MiB live, 11.2MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Outputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Calls

4 calls:

1.0ms	x
1.0ms	(*.f64 x x)
1.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
1.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))

Results

Accuracy	Segments	Branch
52.2%	1	`x`
52.2%	1	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
52.2%	1	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
52.2%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch12.0ms (0.3%)

Memory

-15.7MiB live, 23.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.0035891072538425427	690.9357297908474

Samples

5.0ms

144×

valid

Compiler

Compiled 64 to 91 computations (-42.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-sub: 1.0ms (50.3% of total)

ival-div: 1.0ms (50.3% of total)

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

exact: 0.0ms (0% of total)

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

simplify22.0ms (0.5%)

Memory

15.3MiB live, 54.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	55
1	21	55

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(if (<=.f64 (.f64 x x) #s(literal 3 binary64)) #s(approx (/ (- ( x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x))))
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Outputs
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/6 binary64) x) x #s(literal -1/2 binary64))
(if (<=.f64 (.f64 x x) #s(literal 3 binary64)) #s(approx (/ (- ( x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x))))
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

soundness569.0ms (13.2%)

Memory

-13.0MiB live, 300.1MiB allocated

Rules

5 168×	`lower-/.f32`
5 166×	`lower-/.f64`
4 434×	`lower-fma.f32`
4 428×	`lower-fma.f64`
4 388×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	162
1	43	162
2	98	162
3	236	162
4	759	162
5	1590	162
6	2334	162
7	3514	162
8	4236	162
9	5345	162
10	6402	162
11	7126	162
0	8039	144
0	24	75
0	36	66
1	148	66
2	841	66
3	6272	66
0	8428	66
0	6	15
0	9	15
1	42	15
2	230	15
3	1831	15
0	8685	13

Stop Event

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

Compiler

Compiled 92 to 61 computations (33.7% saved)

preprocess58.0ms (1.3%)

Memory: 25.8MiB live, 67.2MiB allocated
Remove: (abs x)
Compiler: Compiled 106 to 64 computations (39.6% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	8	14
1	31	14
2	69	14
3	166	14
4	292	14
5	371	14
6	397	14
7	405	14
0	6	7
0	9	7
1	16	7
2	22	7
3	24	7
0	24	6

Iter	Nodes	Cost
0	8	14
1	31	14
2	69	14
3	166	14
4	292	14
5	371	14
6	397	14
7	405	14
0	6	7
0	9	7
1	16	7
2	22	7
3	24	7
0	24	6

start0.0ms (0%)

analyze0.0ms (0%)

sample784.0ms (18.2%)

explain65.0ms (1.5%)

preprocess26.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize69.0ms (1.6%)

series3.0ms (0.1%)

simplify155.0ms (3.6%)

rewrite208.0ms (4.8%)

eval99.0ms (2.3%)

prune16.0ms (0.4%)

simplify5.0ms (0.1%)

localize94.0ms (2.2%)

series7.0ms (0.2%)

simplify207.0ms (4.8%)

rewrite434.0ms (10.1%)

eval137.0ms (3.2%)

prune22.0ms (0.5%)

simplify5.0ms (0.1%)

localize56.0ms (1.3%)

series8.0ms (0.2%)

simplify161.0ms (3.7%)

rewrite329.0ms (7.7%)

eval339.0ms (7.9%)

prune20.0ms (0.5%)

simplify4.0ms (0.1%)

localize31.0ms (0.7%)

series4.0ms (0.1%)

simplify149.0ms (3.5%)

rewrite127.0ms (3%)

eval15.0ms (0.3%)

prune6.0ms (0.1%)

regimes17.0ms (0.4%)

regimes11.0ms (0.3%)

regimes8.0ms (0.2%)

regimes7.0ms (0.2%)

regimes5.0ms (0.1%)

bsearch12.0ms (0.3%)

simplify22.0ms (0.5%)

soundness569.0ms (13.2%)

preprocess58.0ms (1.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	14
1	31	14
2	69	14
3	166	14
4	292	14
5	371	14
6	397	14
7	405	14
0	6	7
0	9	7
1	16	7
2	22	7
3	24	7
0	24	6