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

analyze0.0ms (0%)

Memory

0.6MiB live, 0.6MiB 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)

sample639.0ms (11.3%)

Memory

34.7MiB live, 894.2MiB allocated

Samples

379.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 199.0ms

ival-mult: 84.0ms (42.2% of total)

ival-div: 56.0ms (28.2% of total)

ival-sub: 42.0ms (21.1% of total)

exact: 7.0ms (3.5% of total)

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

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

Bogosity

preprocess24.0ms (0.4%)

Memory

10.9MiB live, 47.7MiB 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))
(fma.f64 x (/.f64 x #s(literal 6 binary64)) #s(literal -1/2 binary64))

Symmetry

(abs x)

explain108.0ms (1.9%)

Memory

-5.0MiB 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

25.0ms

512×

valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

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

ival-mult: 7.0ms (51.9% of total)

ival-div: 3.0ms (22.2% of total)

ival-sub: 2.0ms (14.8% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 1 to 1 computations (0% saved)

prune1.0ms (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 8 to 6 computations (25% saved)

simplify5.0ms (0.1%)

Memory

4.3MiB live, 4.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	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))
(fma.f64 x (/.f64 x #s(literal 6 binary64)) #s(literal -1/2 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)

localize24.0ms (0.4%)

Memory

-18.4MiB live, 20.8MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (*.f64 x x) #s(literal 3 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))

Samples

17.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

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

ival-mult: 8.0ms (69.4% of total)

ival-div: 2.0ms (17.4% of total)

ival-sub: 1.0ms (8.7% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

5.4MiB live, 5.4MiB allocated

Counts

3 → 36

Calls

Call 1

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

Outputs
#<alt -3>
#<alt (- (pow x 2) 3)>
#<alt (- (pow x 2) 3)>
#<alt (- (pow x 2) 3)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

9 calls:

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

simplify297.0ms (5.3%)

Memory

3.0MiB live, 249.8MiB 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	235	162
4	748	162
5	1583	162
6	2320	162
7	3495	162
8	4221	162
9	5328	162
10	6382	162
11	7111	162
0	8024	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)
(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) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
(* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))
-1/2
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(- (* 1/6 (pow x 2)) 1/2)
(* 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)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(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))
(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) (- 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))
-1/2
#s(literal -1/2 binary64)
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(- (* 1/6 (pow x 2)) 1/2)
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #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 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #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 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #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)
(*.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)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

rewrite892.0ms (15.8%)

Memory

-33.6MiB live, 558.1MiB allocated

Algorithm

1×	batch-egg-rewrite

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
(+.f64 (*.f64 x x) #s(literal -3 binary64))
(+.f64 #s(literal -3 binary64) (*.f64 x x))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))) (neg.f64 (/.f64 #s(literal 27 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64))))))
(+.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64)))))
(+.f64 (neg.f64 (neg.f64 (*.f64 x x))) #s(literal -3 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -3 binary64)))) #s(literal -1 binary64)))
(-.f64 (*.f64 x x) #s(literal 3 binary64))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 3 binary64) (*.f64 x x)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))) (/.f64 #s(literal 27 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(-.f64 (/.f64 (.f64 x (.f64 x (*.f64 x x))) (fma.f64 x x #s(literal 3 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (.f64 x x) #s(literal -3 binary64)))) (/.f64 #s(literal 27 binary64) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal -3 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 27 binary64)) #s(literal 729 binary64)))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))) (/.f64 (/.f64 #s(literal 19683 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 27 binary64)) #s(literal 729 binary64)))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 27 binary64))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))) (/.f64 (/.f64 #s(literal 729 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 27 binary64))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 27 binary64)) #s(literal 729 binary64)))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (.f64 x x) #s(literal -3 binary64)))) (/.f64 (/.f64 #s(literal 19683 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 27 binary64)) #s(literal 729 binary64)))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal -3 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 27 binary64))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (.f64 x x) #s(literal -3 binary64)))) (/.f64 (/.f64 #s(literal 729 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 27 binary64))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal -3 binary64)))))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))) (/.f64 #s(literal 27 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 27 binary64)) #s(literal 729 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))) (/.f64 (/.f64 #s(literal 19683 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) #s(literal 27 binary64)) #s(literal 729 binary64)))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 27 binary64))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))) (/.f64 (/.f64 #s(literal 729 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 27 binary64))) (neg.f64 (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))))
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(.f64 (/.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) #s(literal 1 binary64))) (/.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -9 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -3 binary64)))))
(.f64 (/.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 27 binary64)))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64))))))
(.f64 (/.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))))) (-.f64 #s(literal 3 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (.f64 x x) #s(literal -3 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)))) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) #s(literal 1 binary64))) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -3 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 27 binary64)))) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (neg.f64 (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (*.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))))) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (fma.f64 x (neg.f64 x) #s(literal -3 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 27 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal 1/6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64)) #s(literal -1 binary64)) (/.f64 #s(literal -1/6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64)))) (/.f64 #s(literal -1/6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64)))) (/.f64 #s(literal -1/6 binary64) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal -3 binary64)))))
(.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -9 binary64)))) (/.f64 #s(literal -1/6 binary64) (fma.f64 x x #s(literal 3 binary64))))
(.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (/.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -9 binary64)) #s(literal 1 binary64))) (/.f64 #s(literal -1/6 binary64) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal -3 binary64)))))
(.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 27 binary64)))) (/.f64 #s(literal 1/6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
(.f64 (/.f64 (neg.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64)) (neg.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -9 binary64))))) (/.f64 #s(literal 1/6 binary64) (fma.f64 x x #s(literal 3 binary64))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 1 binary64)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)

eval72.0ms (1.3%)

Memory: -12.7MiB live, 179.1MiB allocated
Compiler: Compiled 23 906 to 1 639 computations (93.1% saved)

prune66.0ms (1.2%)

Memory

25.3MiB live, 187.8MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	545	7	552
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	546	7	553

Accuracy

100.0%

Counts

553 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
▶	99.9%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
	61.8%	(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
	68.1%	(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))))) #s(literal 6 binary64))
▶	51.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	51.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
▶	49.5%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 142 to 86 computations (39.4% saved)

simplify8.0ms (0.1%)

Memory

-29.4MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Rules

18×	`lower-*.f32`
14×	`lower-fma.f32`
12×	`lower-*.f64`
12×	`lower-+.f64`
12×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	82
0	24	82
1	37	82
2	42	82
3	44	82
0	44	78

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize70.0ms (1.2%)

Memory

11.8MiB live, 90.4MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	accuracy	51.6%	#s(approx (- (* x x) 3) (*.f64 x x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.8%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/6 binary64))
✓	accuracy	51.6%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	accuracy	49.5%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
✓	accuracy	99.9%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	accuracy	99.4%	(*.f64 x #s(literal 1/6 binary64))

Samples

35.0ms

256×

valid

Compiler

Compiled 70 to 15 computations (78.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 6.0ms (39.6% of total)

const: 4.0ms (26.4% of total)

ival-div: 2.0ms (13.2% of total)

ival-add: 2.0ms (13.2% of total)

ival-sub: 1.0ms (6.6% 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

8.4MiB live, 8.4MiB allocated

Counts

9 → 108

Calls

Call 1

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

Outputs
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt -3>
#<alt (- (pow x 2) 3)>
#<alt (- (pow x 2) 3)>
#<alt (- (pow x 2) 3)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>

Calls

27 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(* x 1/6)
0.0ms	x	@	-inf	(* x 1/6)
0.0ms	x	@	0	(* x 1/6)
0.0ms	x	@	inf	(* (* x x) 1/6)
0.0ms	x	@	0	(+ (* (* x 1/6) x) -1/2)

simplify188.0ms (3.3%)

Memory

10.6MiB live, 333.6MiB 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	20	554
1	45	554
2	98	554
3	232	554
4	746	554
5	1580	554
6	2314	554
7	3484	554
8	4207	554
9	5314	554
10	6368	554
11	7101	554
0	8014	500

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

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

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

rewrite417.0ms (7.4%)

Memory

-28.8MiB live, 447.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 952×	`lower-*.f32`
5 946×	`lower-*.f64`
5 706×	`lower-fma.f32`
5 702×	`lower-fma.f64`
3 066×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	65
0	24	65
1	94	63
2	434	63
3	3424	63
0	9026	61

Stop Event

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

Counts

9 → 473

Calls

Call 1

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

Outputs
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(+.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(exp.f64 (.f64 (neg.f64 (log.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))) #s(literal -1 binary64)))
(-.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal -1/6 binary64)))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(-.f64 (/.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64)))) #s(literal 6 binary64)) (/.f64 (/.f64 #s(literal 27 binary64) (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 9 binary64)))) #s(literal 6 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (*.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64)))) #s(literal 6 binary64)) (/.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))) #s(literal 6 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 #s(literal 6 binary64) (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64))))) (/.f64 #s(literal 27 binary64) (.f64 #s(literal 6 binary64) (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 9 binary64))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 #s(literal 6 binary64) (.f64 x x) #s(literal 18 binary64))) (/.f64 #s(literal 9 binary64) (fma.f64 #s(literal 6 binary64) (*.f64 x x) #s(literal 18 binary64))))
(-.f64 (/.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64))) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/12 binary64)) #s(literal 1/4 binary64))) (/.f64 #s(literal 1/8 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/12 binary64)) #s(literal 1/4 binary64))))
(-.f64 (/.f64 #s(literal 1/4 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64)))) (/.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64)))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
(fma.f64 x (/.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 x (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(fma.f64 x (exp.f64 (log.f64 (*.f64 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))
(fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 x (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x)))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 #s(literal 1/6 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (.f64 x (.f64 #s(literal 1/6 binary64) (.f64 x x))) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 x x) (/.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))))
(fma.f64 (*.f64 x x) (exp.f64 (log.f64 #s(literal 1/6 binary64))) #s(literal -1/2 binary64))
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(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64)))) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal -3 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -9 binary64)))) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 3 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal -1/8 binary64)) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) (.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64))))) (fma.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) (-.f64 (fma.f64 (.f64 x x) #s(literal 1/12 binary64) #s(literal 1/4 binary64)) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))))) (.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/1296 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal -1/8 binary64)) (.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/12 binary64)) #s(literal 1/4 binary64)) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/12 binary64))))) (+.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) #s(literal -1/4 binary64)) (.f64 (.f64 x x) #s(literal -1/12 binary64))))
(.f64 (/.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) #s(literal -1/4 binary64)) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal 1/8 binary64))) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) (fma.f64 (*.f64 x x) #s(literal -1/12 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64))) (fma.f64 (.f64 x x) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64)) (.f64 (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64)) (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64)))))) (fma.f64 x (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64)) (-.f64 (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64)) (.f64 x (.f64 x (*.f64 x x)))))))
(.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64))) (.f64 (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -9 binary64)) (.f64 #s(literal 3 binary64) (.f64 x x))))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal -9 binary64)) (.f64 #s(literal 3 binary64) (.f64 x x))))
(.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -9 binary64))) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -9 binary64))) (fma.f64 x x #s(literal -3 binary64)))
(.f64 (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -9 binary64))) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal 27 binary64))) (fma.f64 x (.f64 x (.f64 x x)) (-.f64 #s(literal 9 binary64) (.f64 #s(literal 3 binary64) (.f64 x x)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 #s(literal 6 binary64) (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 9 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -9 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 6 binary64) (.f64 x x) #s(literal 18 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 3 binary64) (.f64 x x))) #s(literal -1 binary64)) #s(literal -1/6 binary64))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/12 binary64)) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64)) #s(literal -1/64 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/1296 binary64) (fma.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1/144 binary64) #s(literal 1/16 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 x (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (fma.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))) #s(literal 1/1296 binary64) #s(literal -1/16 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/12 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x))) (.f64 #s(literal 1/10077696 binary64) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 x (.f64 x x)))) #s(literal -1/512 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64)) #s(literal 1/64 binary64)) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal -1/1728 binary64)))))
(.f64 (pow.f64 (/.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/12 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) #s(literal 1/46656 binary64)) #s(literal -1/64 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal 1/8 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 27 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 6 binary64) (neg.f64 (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) #s(literal -3 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal -6 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal -6 binary64) (fma.f64 x (.f64 x (*.f64 x x)) #s(literal -9 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x (neg.f64 x) #s(literal -3 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/216 binary64)) #s(literal -1/8 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (.f64 x x) (-.f64 (.f64 (*.f64 x x) #s(literal 1/36 binary64)) #s(literal -1/12 binary64)) #s(literal 1/4 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) #s(literal -1/4 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 x x) #s(literal -1/6 binary64) #s(literal -1/2 binary64))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64)))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal -1/6 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (fma.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)) #s(literal -27 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 3 binary64) (.f64 x x) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 9 binary64)))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (fma.f64 x (.f64 x (.f64 x x)) #s(literal -9 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 x x #s(literal 3 binary64))))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal -1/6 binary64)))
(neg.f64 (.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal -1/6 binary64)))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal -1/6 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x)))))
(/.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- (* x x) 3) (*.f64 x x))))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
(/.f64 (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))))
(/.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (- ( x x) 3) (*.f64 x x)))) #s(literal -6 binary64))
(pow.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- ( x x) 3) (*.f64 x x))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- ( x x) 3) (*.f64 x x))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 6 binary64) #s(approx (- ( x x) 3) (.f64 x x))) (/.f64 #s(literal 6 binary64) #s(approx (- ( x x) 3) (*.f64 x x)))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (neg.f64 (log.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- ( x x) 3) (*.f64 x x)))))) #s(literal -1 binary64))
(.f64 #s(literal 1/6 binary64) #s(approx (- ( x x) 3) (*.f64 x x)))
(.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- ( x x) 3) (*.f64 x x)))))
(.f64 #s(literal 1/6 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) #s(approx (- ( x x) 3) (*.f64 x x))) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 #s(approx (- ( x x) 3) (*.f64 x x)) #s(literal 1/6 binary64))
(.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal 1 binary64))
(.f64 (neg.f64 #s(approx (- ( x x) 3) (*.f64 x x))) #s(literal -1/6 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))))
(.f64 #s(literal -1 binary64) (.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal -1/6 binary64)))
(.f64 #s(literal -1/6 binary64) (neg.f64 #s(approx (- ( x x) 3) (*.f64 x x))))
(.f64 #s(literal -1/6 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (- ( x x) 3) (*.f64 x x)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) #s(approx (- ( x x) 3) (*.f64 x x)))) #s(literal 1/6 binary64))
(.f64 (pow.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- (* x x) 3) (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x)))) #s(literal -1/6 binary64))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (neg.f64 #s(approx (- ( x x) 3) (*.f64 x x)))) #s(literal -1 binary64)) #s(literal -1/6 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))))
(neg.f64 (neg.f64 #s(approx (- (* x x) 3) (*.f64 x x))))
#s(approx (- (* x x) 3) (*.f64 x x))
(.f64 #s(literal 1 binary64) #s(approx (- ( x x) 3) (*.f64 x x)))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (- ( x x) 3) (*.f64 x x))))

eval94.0ms (1.7%)

Memory: 39.1MiB live, 114.9MiB allocated
Compiler: Compiled 12 306 to 652 computations (94.7% saved)

prune87.0ms (1.5%)

Memory

5.1MiB live, 79.2MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	615	2	617
Fresh	1	1	2
Picked	1	4	5
Done	0	0	0
Total	617	7	624

Accuracy

100.0%

Counts

624 → 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))
✓	99.8%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
▶	68.1%	(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))))) #s(literal 6 binary64))
✓	51.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	51.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
▶	51.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))
✓	49.5%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 60 to 36 computations (40% saved)

simplify173.0ms (3.1%)

Memory

-24.0MiB live, 98.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓	cost-diff	384	(/.f64 x #s(literal 6 binary64))
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64)))))
✓	cost-diff	128	(neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))))
✓	cost-diff	384	(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))))) #s(literal 6 binary64))
✓	cost-diff	0	(*.f64 x #s(literal 1/6 binary64))
✓	cost-diff	0	(.f64 (.f64 x #s(literal 1/6 binary64)) x)
✓	cost-diff	0	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))

Rules

1 760×	`lower-fma.f32`
1 754×	`lower-fma.f64`
1 328×	`lower-*.f32`
1 320×	`lower-*.f64`
1 008×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	110
0	36	102
1	68	98
2	102	98
3	173	98
4	306	98
5	557	98
6	1109	98
7	3530	98
8	4192	98
9	4312	98
10	4361	98
11	4381	98
12	4389	98
13	4575	98
14	4639	98
15	4647	98
16	4647	98
17	4651	98
0	4651	97

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize90.0ms (1.6%)

Memory

1.1MiB live, 78.4MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 x #s(literal 6 binary64))
✓	accuracy	99.9%	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.2%	(/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64)))
✓	accuracy	91.9%	(fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64)))))
✓	accuracy	77.8%	(/.f64 x (fma.f64 x x #s(literal 3 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x #s(literal 1/6 binary64)) x)
✓	accuracy	99.4%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	51.6%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))

Samples

68.0ms

256×

valid

Compiler

Compiled 117 to 24 computations (79.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-add: 14.0ms (38.1% of total)

ival-mult: 9.0ms (24.5% of total)

ival-div: 8.0ms (21.8% of total)

const: 3.0ms (8.2% of total)

ival-sub: 1.0ms (2.7% of total)

ival-neg: 1.0ms (2.7% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

8.0MiB live, 7.9MiB allocated

Counts

11 → 132

Calls

Call 1

Inputs
#<alt #s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))>
#<alt (.f64 (.f64 x #s(literal 1/6 binary64)) x)>
#<alt (*.f64 x #s(literal 1/6 binary64))>
#<alt (/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))))) #s(literal 6 binary64))>
#<alt (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))))>
#<alt (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64)))))>
#<alt (.f64 x (.f64 x x))>
#<alt (/.f64 x #s(literal 6 binary64))>
#<alt (fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))>
#<alt (/.f64 x (fma.f64 x x #s(literal 3 binary64)))>
#<alt (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64)))>

Outputs
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt -3>
#<alt (- (pow x 2) 3)>
#<alt (- (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) 3)>
#<alt (- (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/9 (pow x 2)) 1/3)))) 3)>
#<alt (/ -9 (pow x 2))>
#<alt (/ (- (* 27 (/ 1 (pow x 2))) 9) (pow x 2))>
#<alt (/ (- (* 27 (/ 1 (pow x 2))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))>
#<alt (/ (- (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6)))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))>
#<alt (/ -9 (pow x 2))>
#<alt (/ (- (* 27 (/ 1 (pow x 2))) 9) (pow x 2))>
#<alt (/ (- (* 27 (/ 1 (pow x 2))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))>
#<alt (/ (- (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6)))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))>
#<alt -3>
#<alt (- (pow x 2) 3)>
#<alt (- (pow x 2) 3)>
#<alt (- (pow x 2) 3)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1 (* 3 (/ 1 (pow x 2)))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/3 x)>
#<alt (* x (+ 1/3 (* -1/9 (pow x 2))))>
#<alt (* x (+ 1/3 (* (pow x 2) (- (* 1/27 (pow x 2)) 1/9))))>
#<alt (* x (+ 1/3 (* (pow x 2) (- (* (pow x 2) (+ 1/27 (* -1/81 (pow x 2)))) 1/9))))>
#<alt (/ 1 x)>
#<alt (/ (- 1 (* 3 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 9 (pow x 4))) (* 3 (/ 1 (pow x 2)))) x)>
#<alt (/ (- (+ 1 (/ 9 (pow x 4))) (+ (* 3 (/ 1 (pow x 2))) (* 27 (/ 1 (pow x 6))))) x)>
#<alt (/ 1 x)>
#<alt (* -1 (/ (- (* 3 (/ 1 (pow x 2))) 1) x))>
#<alt (* -1 (/ (- (* 3 (/ 1 (pow x 2))) (+ 1 (/ 9 (pow x 4)))) x))>
#<alt (* -1 (/ (- (+ (* 3 (/ 1 (pow x 2))) (* 27 (/ 1 (pow x 6)))) (+ 1 (/ 9 (pow x 4)))) x))>
#<alt 3>
#<alt (+ 3 (* -1 (pow x 2)))>
#<alt (+ 3 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))>
#<alt (+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -1/9 (pow x 2)))) 1)))>
#<alt (/ 9 (pow x 2))>
#<alt (/ (- 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 9 (/ 81 (pow x 4))) (* 27 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 9 (/ 81 (pow x 4))) (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 9 (pow x 2))>
#<alt (/ (- 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 9 (/ 81 (pow x 4))) (* 27 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 9 (/ 81 (pow x 4))) (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6))))) (pow x 2))>

Calls

33 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(/ (+ (* (* x (* x x)) (/ x (+ (* x x) 3))) (neg (/ 9 (+ (* x x) 3)))) 6)
1.0ms	x	@	0	(/ (+ (* (* x (* x x)) (/ x (+ (* x x) 3))) (neg (/ 9 (+ (* x x) 3)))) 6)
0.0ms	x	@	-inf	(* x (* x x))
0.0ms	x	@	0	(* x (* x x))
0.0ms	x	@	inf	(/ x (+ (* x x) 3))

simplify373.0ms (6.6%)

Memory

6.1MiB live, 290.9MiB allocated

Algorithm

1×	egg-herbie

Rules

10 800×	`lower-fma.f64`
10 800×	`lower-fma.f32`
2 974×	`lower-*.f64`
2 974×	`lower-*.f32`
2 926×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	112	887
1	299	886
2	754	878
3	2089	878
4	5181	878
0	8233	827

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)
(* 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 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 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)
(* 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)))))
-3
(- (pow x 2) 3)
(- (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) 3)
(- (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/9 (pow x 2)) 1/3)))) 3)
(/ -9 (pow x 2))
(/ (- (* 27 (/ 1 (pow x 2))) 9) (pow x 2))
(/ (- (* 27 (/ 1 (pow x 2))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
(/ (- (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6)))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
(/ -9 (pow x 2))
(/ (- (* 27 (/ 1 (pow x 2))) 9) (pow x 2))
(/ (- (* 27 (/ 1 (pow x 2))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
(/ (- (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6)))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
-3
(- (pow x 2) 3)
(- (pow x 2) 3)
(- (pow x 2) 3)
(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) (- 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 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 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)
(* 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)))))
(* 1/3 x)
(* x (+ 1/3 (* -1/9 (pow x 2))))
(* x (+ 1/3 (* (pow x 2) (- (* 1/27 (pow x 2)) 1/9))))
(* x (+ 1/3 (* (pow x 2) (- (* (pow x 2) (+ 1/27 (* -1/81 (pow x 2)))) 1/9))))
(/ 1 x)
(/ (- 1 (* 3 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 9 (pow x 4))) (* 3 (/ 1 (pow x 2)))) x)
(/ (- (+ 1 (/ 9 (pow x 4))) (+ (* 3 (/ 1 (pow x 2))) (* 27 (/ 1 (pow x 6))))) x)
(/ 1 x)
(* -1 (/ (- (* 3 (/ 1 (pow x 2))) 1) x))
(* -1 (/ (- (* 3 (/ 1 (pow x 2))) (+ 1 (/ 9 (pow x 4)))) x))
(* -1 (/ (- (+ (* 3 (/ 1 (pow x 2))) (* 27 (/ 1 (pow x 6)))) (+ 1 (/ 9 (pow x 4)))) x))
3
(+ 3 (* -1 (pow x 2)))
(+ 3 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -1/9 (pow x 2)))) 1)))
(/ 9 (pow x 2))
(/ (- 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 9 (/ 81 (pow x 4))) (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 9 (/ 81 (pow x 4))) (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6))))) (pow x 2))
(/ 9 (pow x 2))
(/ (- 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 9 (/ 81 (pow x 4))) (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 9 (/ 81 (pow x 4))) (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6))))) (pow x 2))

Outputs
-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))
(* 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))
(* 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))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 (pow x 2))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
-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))
(* 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))
(* 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))
-3
#s(literal -3 binary64)
(- (pow x 2) 3)
(fma.f64 x x #s(literal -3 binary64))
(- (* (pow x 2) (+ 1 (* -1/3 (pow x 2)))) 3)
(fma.f64 x (fma.f64 #s(literal -1/3 binary64) (.f64 x (.f64 x x)) x) #s(literal -3 binary64))
(- (* (pow x 2) (+ 1 (* (pow x 2) (- (* 1/9 (pow x 2)) 1/3)))) 3)
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x (fma.f64 (*.f64 x x) #s(literal 1/9 binary64) #s(literal -1/3 binary64))) #s(literal 1 binary64)) #s(literal -3 binary64))
(/ -9 (pow x 2))
(/.f64 #s(literal -9 binary64) (*.f64 x x))
(/ (- (* 27 (/ 1 (pow x 2))) 9) (pow x 2))
(/.f64 (+.f64 #s(literal -9 binary64) (/.f64 #s(literal 27 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* 27 (/ 1 (pow x 2))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal -9 binary64) (/.f64 #s(literal 27 binary64) (.f64 x x))) (/.f64 #s(literal -81 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (- (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6)))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal -81 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -27 binary64) (.f64 x x))) (/.f64 #s(literal -243 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x x))
(/ -9 (pow x 2))
(/.f64 #s(literal -9 binary64) (*.f64 x x))
(/ (- (* 27 (/ 1 (pow x 2))) 9) (pow x 2))
(/.f64 (+.f64 #s(literal -9 binary64) (/.f64 #s(literal 27 binary64) (.f64 x x))) (.f64 x x))
(/ (- (* 27 (/ 1 (pow x 2))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal -9 binary64) (/.f64 #s(literal 27 binary64) (.f64 x x))) (/.f64 #s(literal -81 binary64) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (- (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6)))) (+ 9 (/ 81 (pow x 4)))) (pow x 2))
(/.f64 (-.f64 (/.f64 #s(literal -81 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -27 binary64) (.f64 x x))) (/.f64 #s(literal -243 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))) (.f64 x x))
-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) (- 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) (- 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 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
(* 1/6 x)
(*.f64 #s(literal 1/6 binary64) x)
-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))
(* 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))
(* 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))
(* 1/3 x)
(*.f64 x #s(literal 1/3 binary64))
(* x (+ 1/3 (* -1/9 (pow x 2))))
(.f64 x (fma.f64 (.f64 x x) #s(literal -1/9 binary64) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (- (* 1/27 (pow x 2)) 1/9))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 x (*.f64 x #s(literal 1/27 binary64)) #s(literal -1/9 binary64)) #s(literal 1/3 binary64)))
(* x (+ 1/3 (* (pow x 2) (- (* (pow x 2) (+ 1/27 (* -1/81 (pow x 2)))) 1/9))))
(.f64 x (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (.f64 x x) #s(literal -1/81 binary64) #s(literal 1/27 binary64)) #s(literal -1/9 binary64)) #s(literal 1/3 binary64)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (- 1 (* 3 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3 binary64) (*.f64 x x))) x)
(/ (- (+ 1 (/ 9 (pow x 4))) (* 3 (/ 1 (pow x 2)))) x)
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3 binary64) (.f64 x x))) (/.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(/ (- (+ 1 (/ 9 (pow x 4))) (+ (* 3 (/ 1 (pow x 2))) (* 27 (/ 1 (pow x 6))))) x)
(/.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3 binary64) (.f64 x x))) (/.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -27 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(* -1 (/ (- (* 3 (/ 1 (pow x 2))) 1) x))
(/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3 binary64) (*.f64 x x))) x)
(* -1 (/ (- (* 3 (/ 1 (pow x 2))) (+ 1 (/ 9 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3 binary64) (.f64 x x))) (/.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 x x))))) x)
(* -1 (/ (- (+ (* 3 (/ 1 (pow x 2))) (* 27 (/ 1 (pow x 6)))) (+ 1 (/ 9 (pow x 4)))) x))
(/.f64 (+.f64 (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -3 binary64) (.f64 x x))) (/.f64 #s(literal 9 binary64) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal -27 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))) x)
3
#s(literal 3 binary64)
(+ 3 (* -1 (pow x 2)))
(-.f64 #s(literal 3 binary64) (*.f64 x x))
(+ 3 (* (pow x 2) (- (* 1/3 (pow x 2)) 1)))
(fma.f64 (.f64 x x) (fma.f64 x (.f64 x #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))
(+ 3 (* (pow x 2) (- (* (pow x 2) (+ 1/3 (* -1/9 (pow x 2)))) 1)))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (*.f64 x x) #s(literal -1/9 binary64) #s(literal 1/3 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))
(/ 9 (pow x 2))
(/.f64 #s(literal 9 binary64) (*.f64 x x))
(/ (- 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -27 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 9 (/ 81 (pow x 4))) (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 81 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -27 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 9 (/ 81 (pow x 4))) (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 9 binary64) (+.f64 (/.f64 #s(literal 81 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -27 binary64) (.f64 x x)) (/.f64 #s(literal -243 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x x))
(/ 9 (pow x 2))
(/.f64 #s(literal 9 binary64) (*.f64 x x))
(/ (- 9 (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -27 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 9 (/ 81 (pow x 4))) (* 27 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 (/.f64 #s(literal 81 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 #s(literal 9 binary64) (/.f64 #s(literal -27 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 9 (/ 81 (pow x 4))) (+ (* 27 (/ 1 (pow x 2))) (* 243 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 9 binary64) (+.f64 (/.f64 #s(literal 81 binary64) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal -27 binary64) (.f64 x x)) (/.f64 #s(literal -243 binary64) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x x))

rewrite393.0ms (6.9%)

Memory

-2.6MiB live, 466.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 040×	`lower-fma.f32`
6 034×	`lower-fma.f64`
3 814×	`lower-/.f32`
3 806×	`lower-/.f64`
3 648×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	94
0	36	75
1	141	61
2	941	61
0	8499	60

Stop Event

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

Counts

11 → 705

Calls

Call 1

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

Outputs
#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
(neg.f64 (.f64 (.f64 x x) #s(literal -1/6 binary64)))
(neg.f64 (.f64 (.f64 x #s(literal -1/6 binary64)) x))
(neg.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))))
(/.f64 x (/.f64 #s(literal 6 binary64) x))
(/.f64 (*.f64 x x) #s(literal 6 binary64))
(/.f64 (neg.f64 x) (/.f64 #s(literal -6 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 6 binary64) x) x))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x))))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -6 binary64))
(/.f64 (neg.f64 (*.f64 x (neg.f64 x))) #s(literal 6 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) #s(literal -1 binary64))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(*.f64 #s(literal 1/6 binary64) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(.f64 (.f64 x #s(literal 1/6 binary64)) x)
(.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/6 binary64) (*.f64 x x)))
(.f64 (.f64 x (neg.f64 x)) #s(literal -1/6 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 6 binary64) x)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/6 binary64)))
(neg.f64 (*.f64 x #s(literal -1/6 binary64)))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal -1/6 binary64))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 6 binary64) x)))
(/.f64 x #s(literal 6 binary64))
(/.f64 (neg.f64 x) #s(literal -6 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) x))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -6 binary64) x))
(pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1 binary64))
(*.f64 x #s(literal 1/6 binary64))
(*.f64 #s(literal 1/6 binary64) x)
(*.f64 #s(literal 1/6 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 (neg.f64 x) #s(literal -1/6 binary64))
(.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/6 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x #s(literal -1/6 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1/2 binary64)))
(+.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(+.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64))) (neg.f64 (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64)))))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x (/.f64 x (fma.f64 x x #s(literal 3 binary64)))))) #s(literal 1/6 binary64)) (neg.f64 (*.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))) #s(literal 1/6 binary64))))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x (/.f64 x (fma.f64 x x #s(literal 3 binary64)))))) #s(literal 1/6 binary64)) (*.f64 (/.f64 #s(literal -9 binary64) (fma.f64 x x #s(literal 3 binary64))) #s(literal 1/6 binary64)))
(+.f64 (.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -9 binary64) (fma.f64 x x #s(literal 3 binary64)))) (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x (*.f64 x (/.f64 x (fma.f64 x x #s(literal 3 binary64))))))))
(+.f64 (.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x (.f64 x (/.f64 x (fma.f64 x x #s(literal 3 binary64))))))) (*.f64 #s(literal 1/6 binary64) (/.f64 #s(literal -9 binary64) (fma.f64 x x #s(literal 3 binary64)))))
(+.f64 (.f64 (/.f64 #s(literal -9 binary64) (fma.f64 x x #s(literal 3 binary64))) #s(literal 1/6 binary64)) (.f64 (.f64 x (.f64 x (*.f64 x (/.f64 x (fma.f64 x x #s(literal 3 binary64)))))) #s(literal 1/6 binary64)))
(+.f64 (.f64 (.f64 #s(literal 1/6 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1/2 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 #s(literal 6 binary64) (fma.f64 x x #s(literal -3 binary64)))) #s(literal -1 binary64)))
(-.f64 (.f64 #s(literal 1/6 binary64) (.f64 x x)) #s(literal 1/2 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal -1/6 binary64)))
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) #s(literal 1/36 binary64))) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64))) (/.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/6 binary64) (.f64 x x) #s(literal 1/2 binary64))))
(-.f64 (.f64 (.f64 x (.f64 x (.f64 x (/.f64 x (fma.f64 x x #s(literal 3 binary64)))))) #s(literal 1/6 binary64)) (*.f64 (/.f64 #s(literal 9 binary64) (fma.f64 x x #s(literal 3 binary64))) #s(literal 1/6 binary64)))
(-.f64 (/.f64 (/.f64 (/.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (fma.f64 x x #s(literal 3 binary64)) (fma.f64 x x #s(literal 3 binary64)))) (/.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64)) (fma.f64 x x #s(literal 3 binary64)))) #s(literal 6 binary64)) (/.f64 (/.f64 (/.f64 #s(literal 81 binary64) (.f64 (fma.f64 x x #s(literal 3 binary64)) (fma.f64 x x #s(literal 3 binary64)))) (/.f64 (fma.f64 (.f64 x x) (*.f64 x x) #s(literal 9 binary64)) (fma.f64 x x #s(literal 3 binary64)))) #s(literal 6 binary64)))
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(.f64 (/.f64 #s(literal -9 binary64) (fma.f64 (.f64 x x) (.f64 x x) #s(literal -9 binary64))) (-.f64 #s(literal 3 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 9 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) #s(literal 27 binary64))) (+.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal -3 binary64))))
(.f64 (/.f64 #s(literal 9 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -9 binary64))) (fma.f64 x x #s(literal -3 binary64)))
(.f64 (pow.f64 (.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 1/9 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 1/9 binary64)) #s(literal -1/2 binary64)))
(.f64 (neg.f64 (/.f64 #s(literal -9 binary64) (fma.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)) #s(literal 27 binary64)))) (+.f64 (fma.f64 (.f64 x x) (.f64 x x) #s(literal 9 binary64)) (.f64 (*.f64 x x) #s(literal -3 binary64))))
(.f64 (neg.f64 (/.f64 #s(literal -9 binary64) (fma.f64 (.f64 x x) (*.f64 x x) #s(literal -9 binary64)))) (fma.f64 x x #s(literal -3 binary64)))

eval110.0ms (1.9%)

Memory: 24.7MiB live, 221.6MiB allocated
Compiler: Compiled 25 790 to 1 973 computations (92.3% saved)

prune76.0ms (1.3%)

Memory

-38.8MiB live, 204.4MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	835	2	837
Fresh	0	0	0
Picked	2	1	3
Done	0	4	4
Total	837	7	844

Accuracy

100.0%

Counts

844 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	51.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	51.5%	#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
▶	51.5%	#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))
✓	51.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	51.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))
✓	49.5%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 45 to 27 computations (40% saved)

simplify5.0ms (0.1%)

Memory

11.0MiB live, 11.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 6 binary64) x)
✓	cost-diff	0	#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
✓	cost-diff	384	(/.f64 x (/.f64 #s(literal 6 binary64) x))
✓	cost-diff	0	(/.f64 x #s(literal 6 binary64))
✓	cost-diff	0	(*.f64 (/.f64 x #s(literal 6 binary64)) x)
✓	cost-diff	0	#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	46
0	16	46
1	25	46
2	29	46
3	30	46
0	30	44

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize30.0ms (0.5%)

Memory

26.2MiB live, 65.4MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 #s(literal 6 binary64) x)
✓	accuracy	99.8%	(/.f64 x (/.f64 #s(literal 6 binary64) x))
✓	accuracy	51.6%	#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
✓	accuracy	100.0%	(/.f64 x #s(literal 6 binary64))
✓	accuracy	99.8%	(*.f64 (/.f64 x #s(literal 6 binary64)) x)
✓	accuracy	51.6%	#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))

Samples

19.0ms

256×

valid

Compiler

Compiled 36 to 12 computations (66.7% saved)

Precisions

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

ival-div: 6.0ms (55.1% of total)

ival-mult: 3.0ms (27.5% of total)

ival-sub: 1.0ms (9.2% 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

-35.1MiB live, 4.2MiB allocated

Counts

6 → 72

Calls

Call 1

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

Outputs
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 x)>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt -1/2>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (- (* 1/6 (pow x 2)) 1/2)>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- 1/6 (* 1/2 (/ 1 (pow x 2)))))>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>
#<alt (/ 6 x)>

Calls

18 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/ 6 x)
0.0ms	x	@	inf	(/ 6 x)
0.0ms	x	@	-inf	(/ 6 x)
0.0ms	x	@	0	(/ x (/ 6 x))
0.0ms	x	@	inf	(/ x (/ 6 x))

simplify166.0ms (2.9%)

Memory

4.6MiB live, 252.0MiB allocated

Algorithm

1×	egg-herbie

Rules

3 346×	`lower-*.f64`
3 346×	`lower-*.f32`
2 718×	`lower-fma.f64`
2 718×	`lower-fma.f32`
1 532×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	340
1	31	340
2	60	340
3	133	340
4	375	340
5	708	340
6	1165	340
7	2183	340
8	3647	340
9	4736	340
10	5698	340
11	6854	340
0	8021	322

Stop Event

1×	iter limit
1×	node limit

Counts

72 → 72

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)
(* 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 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 x)
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (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)
(* 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)))))
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)
(/ 6 x)

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

rewrite218.0ms (3.8%)

Memory

16.2MiB live, 406.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 070×	`lower-*.f32`
4 068×	`lower-*.f64`
3 656×	`lower-/.f32`
3 650×	`lower-/.f64`
2 808×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	42
0	16	42
1	63	42
2	327	42
3	2725	42
0	8148	40

Stop Event

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

Counts

6 → 188

Calls

Call 1

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

Outputs
#s(approx (/ (- (* x x) 3) 6) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(exp.f64 (log.f64 (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(exp.f64 (-.f64 (log.f64 (.f64 x #s(literal 1/6 binary64))) (.f64 (log.f64 x) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 6 binary64) x)) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(neg.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 x (/.f64 #s(literal 6 binary64) x))
(/.f64 (*.f64 x x) #s(literal 6 binary64))
(/.f64 (*.f64 x #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) x))
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(/.f64 (*.f64 x (neg.f64 x)) #s(literal -6 binary64))
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(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (.f64 (/.f64 #s(literal -6 binary64) x) (.f64 x #s(literal 1/6 binary64)))) (/.f64 #s(literal 6 binary64) (.f64 x x)))
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(-.f64 #s(literal 0 binary64) (*.f64 x #s(literal -1/6 binary64)))
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(pow.f64 (*.f64 (/.f64 #s(literal 6 binary64) x) (/.f64 #s(literal 6 binary64) x)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(*.f64 x #s(literal 1/6 binary64))
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(*.f64 #s(literal 1/6 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
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(*.f64 #s(literal -1/6 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (log.f64 (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(exp.f64 (-.f64 (log.f64 (.f64 x #s(literal 1/6 binary64))) (.f64 (log.f64 x) #s(literal -1 binary64))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 6 binary64) x)) (.f64 x (.f64 x #s(literal -1/6 binary64))))
(neg.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64)))))
(/.f64 x (/.f64 #s(literal 6 binary64) x))
(/.f64 (*.f64 x x) #s(literal 6 binary64))
(/.f64 (*.f64 x #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))
(/.f64 (neg.f64 x) (/.f64 #s(literal -6 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(/.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -6 binary64) (*.f64 x x)))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -6 binary64))
(/.f64 #s(literal -1/6 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (.f64 x (.f64 x #s(literal -1/6 binary64))) #s(literal -1 binary64))
(/.f64 (*.f64 x #s(literal -1/6 binary64)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal -6 binary64) x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x))) #s(literal -6 binary64))
(/.f64 (neg.f64 (*.f64 x (neg.f64 x))) #s(literal 6 binary64))
(/.f64 (/.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -6 binary64))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal -6 binary64) x)) (.f64 (/.f64 #s(literal -6 binary64) x) x)) (*.f64 (/.f64 #s(literal 6 binary64) x) (/.f64 #s(literal 6 binary64) x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (.f64 (/.f64 #s(literal -6 binary64) x) (.f64 x #s(literal 1/6 binary64)))) (/.f64 #s(literal 6 binary64) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 6 binary64) x)) (.f64 (/.f64 #s(literal -6 binary64) x) (neg.f64 x))) (*.f64 (/.f64 #s(literal -6 binary64) x) (/.f64 #s(literal 6 binary64) x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal -6 binary64) (.f64 x x))) (.f64 (/.f64 #s(literal -6 binary64) x) #s(literal 1 binary64))) (.f64 (/.f64 #s(literal -6 binary64) x) (/.f64 #s(literal -6 binary64) (*.f64 x x))))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 (/.f64 #s(literal -6 binary64) x) (.f64 x #s(literal -1/6 binary64)))) (/.f64 #s(literal -6 binary64) (.f64 x x)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (/.f64 #s(literal 6 binary64) x)) (.f64 (/.f64 #s(literal -6 binary64) x) (/.f64 x #s(literal -1 binary64)))) (*.f64 (/.f64 #s(literal -6 binary64) x) (/.f64 #s(literal 6 binary64) x)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 #s(literal -6 binary64) x) (/.f64 x (/.f64 #s(literal -1 binary64) x)))) (.f64 (/.f64 #s(literal -6 binary64) x) #s(literal 6 binary64)))
(/.f64 (-.f64 #s(literal 0 binary64) (.f64 (/.f64 #s(literal -6 binary64) x) (.f64 x x))) (*.f64 (/.f64 #s(literal -6 binary64) x) #s(literal -6 binary64)))
(/.f64 (neg.f64 (*.f64 (neg.f64 x) #s(literal 1 binary64))) (/.f64 #s(literal 6 binary64) x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x)))) #s(literal 6 binary64))
(/.f64 (neg.f64 (neg.f64 (*.f64 x (neg.f64 x)))) #s(literal -6 binary64))
(/.f64 (neg.f64 (/.f64 x (/.f64 #s(literal -1 binary64) x))) #s(literal 6 binary64))
(pow.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 6 binary64) (.f64 x x)) (/.f64 #s(literal 6 binary64) (*.f64 x x))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(.f64 (.f64 x #s(literal 1/6 binary64)) x)
(.f64 (.f64 x #s(literal 1/6 binary64)) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))
(.f64 (neg.f64 x) (.f64 x #s(literal -1/6 binary64)))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(.f64 #s(literal 1/6 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x #s(literal -1/6 binary64))))
(.f64 (.f64 x (neg.f64 x)) #s(literal -1/6 binary64))
(.f64 #s(literal -1/6 binary64) (.f64 x (neg.f64 x)))
(*.f64 #s(literal -1/6 binary64) (/.f64 x (/.f64 #s(literal -1 binary64) x)))
(.f64 #s(literal -1/6 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x))) #s(literal -1 binary64)))
(*.f64 #s(literal -1/6 binary64) (pow.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) x) #s(literal -1 binary64)))
(.f64 (.f64 x #s(literal -1/6 binary64)) (neg.f64 x))
(.f64 (/.f64 x #s(literal -1 binary64)) (.f64 x #s(literal -1/6 binary64)))
(*.f64 (/.f64 x (/.f64 #s(literal -1 binary64) x)) #s(literal -1/6 binary64))
(.f64 (/.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64)) (neg.f64 x))
(.f64 (pow.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)) (pow.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1/2 binary64)))
(.f64 (.f64 (*.f64 x #s(literal -1/6 binary64)) #s(literal -1 binary64)) x)
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (neg.f64 x))) #s(literal -1 binary64)) #s(literal -1/6 binary64))
#s(approx (/ (- (* x x) 3) 6) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(exp.f64 (neg.f64 (log.f64 (*.f64 x #s(literal 1/6 binary64)))))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 #s(literal -6 binary64) x))
(neg.f64 (/.f64 #s(literal -6 binary64) x))
(neg.f64 (/.f64 (/.f64 #s(literal 6 binary64) x) #s(literal -1 binary64)))
(/.f64 #s(literal 6 binary64) x)
(/.f64 (/.f64 #s(literal 6 binary64) x) #s(literal 1 binary64))
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(/.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/6 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/6 binary64))
(/.f64 #s(literal -1 binary64) (*.f64 x #s(literal -1/6 binary64)))
(/.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -1/6 binary64))
(pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 6 binary64) x) #s(literal 1 binary64))
(pow.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x #s(literal 1/6 binary64)) (*.f64 x #s(literal 1/6 binary64))) #s(literal -1/2 binary64))
(*.f64 #s(literal 6 binary64) (/.f64 #s(literal 1 binary64) x))
(*.f64 #s(literal 6 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 #s(literal 6 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))
(*.f64 #s(literal 6 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 #s(literal 6 binary64) x) #s(literal 1 binary64))
(*.f64 #s(literal -6 binary64) (/.f64 #s(literal -1 binary64) x))
(*.f64 #s(literal -6 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)))
(*.f64 #s(literal -6 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)))
(*.f64 #s(literal -6 binary64) (pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) x))
(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 6 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -6 binary64) x))
(*.f64 (/.f64 #s(literal -1 binary64) x) #s(literal -6 binary64))
(.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)) #s(literal 6 binary64))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 1 binary64)) #s(literal -6 binary64))
(.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal 1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)))

eval27.0ms (0.5%)

Memory: 12.9MiB live, 54.7MiB allocated
Compiler: Compiled 2 335 to 286 computations (87.8% saved)

prune20.0ms (0.4%)

Memory

-30.7MiB live, 47.2MiB allocated

Pruning

7 alts after pruning (0 fresh and 7 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	0	0
Picked	0	2	2
Done	0	5	5
Total	260	7	267

Accuracy

100.0%

Counts

267 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.8%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	51.5%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	51.5%	#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
✓	51.5%	#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))
✓	51.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	51.5%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))
✓	49.5%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 141 to 61 computations (56.7% saved)

regimes15.0ms (0.3%)

Memory

29.8MiB live, 29.8MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))
#s(approx (/ (- (* x x) 3) 6) (.f64 (.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))
#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))
(/.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))
#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/36 binary64) #s(literal -1/4 binary64)) (fma.f64 (.f64 x x) #s(literal 1/6 binary64) #s(literal 1/2 binary64)))
(/.f64 (fma.f64 (.f64 x (.f64 x x)) (/.f64 x (fma.f64 x x #s(literal 3 binary64))) (neg.f64 (/.f64 #s(literal 9 binary64) (fma.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))

Calls

4 calls:

4.0ms	x
4.0ms	(*.f64 x x)
3.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
3.0ms	(-.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 20 to 13 computations (35% saved)

regimes38.0ms (0.7%)

Memory

-13.2MiB live, 26.1MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

29.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))
3.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(/.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 20 to 13 computations (35% saved)

regimes10.0ms (0.2%)

Memory

20.0MiB live, 20.0MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	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
99.9%	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 20 to 13 computations (35% saved)

regimes59.0ms (1%)

Memory

-13.4MiB live, 32.3MiB 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 (*.f64 x #s(literal 1/6 binary64)) x))

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

Calls

4 calls:

53.0ms	(*.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
99.2%	2	`x`
99.2%	2	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
99.2%	2	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
99.2%	2	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

regimes6.0ms (0.1%)

Memory

-23.3MiB live, 15.6MiB 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:

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

Results

Accuracy	Segments	Branch
49.5%	1	`x`
49.5%	1	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
49.5%	1	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
49.5%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.8597705487780543	31207157288.956364

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify6.0ms (0.1%)

Memory

14.5MiB live, 14.5MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
4×	`+-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	56
1	28	56
2	32	56
3	34	56
4	35	56

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness785.0ms (13.9%)

Memory

6.5MiB live, 388.0MiB allocated

Rules

5 952×	`lower-*.f32`
5 946×	`lower-*.f64`
5 706×	`lower-fma.f32`
5 702×	`lower-fma.f64`
5 168×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	162
1	43	162
2	98	162
3	235	162
4	748	162
5	1583	162
6	2320	162
7	3495	162
8	4221	162
9	5328	162
10	6382	162
11	7111	162
0	8024	144
0	17	65
0	24	65
1	94	63
2	434	63
3	3424	63
0	9026	61
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 94 to 56 computations (40.4% saved)

preprocess54.0ms (1%)

Memory: 21.1MiB live, 105.2MiB allocated
Remove: (abs x)
Compiler: Compiled 120 to 68 computations (43.3% 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

analyze0.0ms (0%)

sample639.0ms (11.3%)

preprocess24.0ms (0.4%)

explain108.0ms (1.9%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize24.0ms (0.4%)

series2.0ms (0%)

simplify297.0ms (5.3%)

rewrite892.0ms (15.8%)

eval72.0ms (1.3%)

prune66.0ms (1.2%)

simplify8.0ms (0.1%)

localize70.0ms (1.2%)

series3.0ms (0.1%)

simplify188.0ms (3.3%)

rewrite417.0ms (7.4%)

eval94.0ms (1.7%)

prune87.0ms (1.5%)

simplify173.0ms (3.1%)

localize90.0ms (1.6%)

series6.0ms (0.1%)

simplify373.0ms (6.6%)

rewrite393.0ms (6.9%)

eval110.0ms (1.9%)

prune76.0ms (1.3%)

simplify5.0ms (0.1%)

localize30.0ms (0.5%)

series3.0ms (0.1%)

simplify166.0ms (2.9%)

rewrite218.0ms (3.8%)

eval27.0ms (0.5%)

prune20.0ms (0.4%)

regimes15.0ms (0.3%)

regimes38.0ms (0.7%)

regimes10.0ms (0.2%)

regimes59.0ms (1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

soundness785.0ms (13.9%)

preprocess54.0ms (1%)

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