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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB 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)

sample953.0ms (17.5%)

Memory

-174.9MiB live, 961.6MiB allocated

Samples

746.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 340.0ms

ival-mult: 206.0ms (60.6% of total)

ival-div: 61.0ms (18% of total)

ival-sub: 56.0ms (16.5% of total)

exact: 9.0ms (2.6% of total)

ival-true: 6.0ms (1.8% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

preprocess23.0ms (0.4%)

Memory

-3.5MiB live, 34.7MiB 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)

explain80.0ms (1.5%)

Memory

40.4MiB live, 161.1MiB 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

29.0ms

512×

valid

Compiler

Compiled 56 to 28 computations (50% saved)

Precisions

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

ival-mult: 4.0ms (36.2% of total)

ival-sub: 3.0ms (27.2% of total)

ival-div: 3.0ms (27.2% of total)

exact: 1.0ms (9.1% of total)

ival-true: 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

1.6MiB live, 1.6MiB 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)

simplify11.0ms (0.2%)

Memory

-26.3MiB live, 10.0MiB 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)

localize56.0ms (1%)

Memory

-1.6MiB live, 34.6MiB allocated

Localize:

Found 3 expressions of interest:

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

Samples

11.0ms

256×

valid

Compiler

Compiled 20 to 8 computations (60% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-div: 2.0ms (38.2% of total)

ival-mult: 2.0ms (38.2% of total)

ival-sub: 1.0ms (19.1% of total)

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

exact: 0.0ms (0% of total)

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

series2.0ms (0%)

Memory

3.0MiB live, 3.0MiB 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	@	inf	(- (* x x) 3)
0.0ms	x	@	0	(/ (- (* x x) 3) 6)
0.0ms	x	@	0	(- (* x x) 3)
0.0ms	x	@	inf	(/ (- (* x x) 3) 6)
0.0ms	x	@	inf	(* x x)

simplify206.0ms (3.8%)

Memory

16.8MiB live, 335.2MiB 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)

rewrite488.0ms (9%)

Memory

-7.9MiB live, 595.6MiB 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)

eval70.0ms (1.3%)

Memory: 17.6MiB live, 141.5MiB allocated
Compiler: Compiled 23 906 to 1 639 computations (93.1% saved)

prune67.0ms (1.2%)

Memory

-27.7MiB live, 172.3MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	546	6	552
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	547	6	553

Accuracy

100.0%

Counts

553 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
	55.9%	(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 27 binary64)) (.f64 #s(literal -6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
▶	54.1%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	99.9%	(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
▶	54.1%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
▶	46.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 122 to 68 computations (44.3% saved)

simplify6.0ms (0.1%)

Memory

11.2MiB live, 11.3MiB 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 #s(literal 1/6 binary64))
✓	cost-diff	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #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	(fma.f64 x x #s(literal -3 binary64))
✓	cost-diff	(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	83
0	27	79
1	42	79
2	48	79
3	50	79
0	50	79

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize50.0ms (0.9%)

Memory

21.7MiB live, 100.2MiB 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	54.2%	#s(approx (- (* x x) 3) (*.f64 x x))
✓	accuracy	99.9%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	accuracy	99.6%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(.f64 (.f64 x x) #s(literal 1/6 binary64))
✓	accuracy	54.2%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	accuracy	46.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(fma.f64 x x #s(literal -3 binary64))
✓	accuracy	99.9%	(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))

Samples

29.0ms

256×

valid

Compiler

Compiled 72 to 17 computations (76.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 8.0ms (46.3% of total)

const: 3.0ms (17.4% of total)

ival-div: 2.0ms (11.6% of total)

ival-add: 2.0ms (11.6% of total)

ival-sub: 1.0ms (5.8% of total)

exact: 1.0ms (5.8% of total)

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

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

series5.0ms (0.1%)

Memory

-34.7MiB live, 6.0MiB allocated

Counts

10 → 120

Calls

Call 1

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

30 calls:

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

simplify285.0ms (5.2%)

Memory

0.8MiB live, 197.6MiB 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	606
1	45	606
2	98	606
3	232	606
4	755	606
5	1591	606
6	2331	606
7	3505	606
8	4228	606
9	5341	606
10	6398	606
11	7131	606
0	8044	543

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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)))))
-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)))))
-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)))))
(* 1/6 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) 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))
-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 #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))
(* 1/6 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) 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))

rewrite936.0ms (17.2%)

Memory

-5.4MiB live, 447.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

6 244×	`lower-fma.f32`
6 240×	`lower-fma.f64`
6 230×	`lower-*.f32`
6 222×	`lower-*.f64`
3 212×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	69
0	27	65
1	95	65
2	512	65
3	4241	65
0	10225	65

Stop Event

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

Counts

10 → 567

Calls

Call 1

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

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 (.f64 x (.f64 x (.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 (.f64 x (.f64 x (.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 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64))) #s(literal 6 binary64)) (/.f64 (/.f64 #s(literal 27 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64))) #s(literal 6 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (*.f64 x 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 x (.f64 x (.f64 x (.f64 x (.f64 x x))))) (.f64 #s(literal 6 binary64) (fma.f64 (.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #s(literal 9 binary64)))) (/.f64 #s(literal 27 binary64) (.f64 #s(literal 6 binary64) (fma.f64 (*.f64 x x) (fma.f64 x x #s(literal 3 binary64)) #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 x) (.f64 (.f64 x (.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 #s(literal 1/6 binary64) (.f64 x x)))) (/.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) #s(literal 1/36 binary64)) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal 1/6 binary64) (.f64 x x)))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
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(/.f64 x #s(literal 6 binary64))
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(*.f64 #s(literal 1/6 binary64) x)
(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)))
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(/.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))
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(pow.f64 (/.f64 #s(literal 6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal -1 binary64))
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(.f64 (.f64 #s(literal 1/6 binary64) #s(approx (- (* x x) 3) (*.f64 x x))) #s(literal 1 binary64))
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(.f64 #s(literal -1/6 binary64) (neg.f64 #s(approx (- ( x x) 3) (*.f64 x x))))
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(.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)))
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eval102.0ms (1.9%)

Memory: 6.7MiB live, 194.6MiB allocated
Compiler: Compiled 15 073 to 934 computations (93.8% saved)

prune77.0ms (1.4%)

Memory

16.0MiB live, 149.6MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	702	3	705
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	703	8	711

Accuracy

100.0%

Counts

711 → 8

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 #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	54.1%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	99.9%	(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
▶	53.9%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/6 binary64)))))
✓	54.1%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
▶	54.1%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))
✓	46.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 54 to 35 computations (35.2% saved)

simplify8.0ms (0.2%)

Memory

-28.2MiB live, 9.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 x #s(literal 6 binary64))
✓	cost-diff	0	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/6 binary64))))
✓	cost-diff	0	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/6 binary64)))))
✓	cost-diff	12800	(exp.f64 (log.f64 #s(literal 1/6 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

18×	`lower-*.f32`
10×	`lower-*.f64`
8×	`*-commutative`
8×	`lower-+.f64`
8×	`lift-*.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	67
0	27	62
1	43	59
2	45	59
0	45	59

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

localize86.0ms (1.6%)

Memory

38.6MiB live, 115.4MiB 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	100.0%	(log.f64 #s(literal 1/6 binary64))
✓	accuracy	99.7%	(.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/6 binary64))))
✓	accuracy	98.4%	(exp.f64 (log.f64 #s(literal 1/6 binary64)))
✓	accuracy	54.2%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/6 binary64)))))
✓	accuracy	99.8%	(.f64 (.f64 x #s(literal 1/6 binary64)) x)
✓	accuracy	99.6%	(*.f64 x #s(literal 1/6 binary64))
✓	accuracy	54.2%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))

Samples

69.0ms

256×

valid

Compiler

Compiled 56 to 18 computations (67.9% saved)

Precisions

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

ival-add: 34.0ms (58% of total)

ival-mult: 8.0ms (13.6% of total)

const: 4.0ms (6.8% of total)

ival-div: 3.0ms (5.1% of total)

ival-exp: 3.0ms (5.1% of total)

ival-sub: 3.0ms (5.1% of total)

ival-log: 3.0ms (5.1% of total)

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

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

exact: 0.0ms (0% of total)

series34.0ms (0.6%)

Memory

-37.5MiB live, 3.3MiB allocated

Counts

10 → 96

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

Calls

24 calls:

Time	Variable		Point	Expression
33.0ms	x	@	-inf	(* (* x x) (exp (log 1/6)))
0.0ms	x	@	0	(+ (* (/ x 6) x) -1/2)
0.0ms	x	@	inf	(+ (* (/ x 6) x) -1/2)
0.0ms	x	@	0	(/ (- (* x x) 3) 6)
0.0ms	x	@	-inf	(+ (* (/ x 6) x) -1/2)

simplify197.0ms (3.6%)

Memory

20.5MiB live, 289.4MiB allocated

Algorithm

1×	egg-herbie

Rules

3 316×	`lower-*.f64`
3 316×	`lower-*.f32`
2 710×	`lower-fma.f64`
2 710×	`lower-fma.f32`
1 534×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	450
1	29	450
2	58	450
3	131	450
4	369	450
5	708	450
6	1172	450
7	2182	450
8	3667	450
9	4761	450
10	5728	450
11	6864	450
0	8036	423

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

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)))))
(* 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)))))
(* 1/6 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)

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))
(* 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))
(* 1/6 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)

rewrite314.0ms (5.8%)

Memory

2.0MiB live, 514.5MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 490×	`lower-/.f32`
4 488×	`lower-/.f64`
4 410×	`lower-fma.f32`
4 408×	`lower-fma.f64`
3 664×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	60
0	27	55
1	87	52
2	435	52
3	4145	52
0	9060	52

Stop Event

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

Counts

10 → 363

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

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 (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal -1 binary64)))
(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 (*.f64 x x) (exp.f64 (log.f64 #s(literal 6 binary64))))
(/.f64 (*.f64 x #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.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) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -6 binary64))
(/.f64 (neg.f64 (*.f64 x #s(literal 1/6 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (*.f64 x (neg.f64 x))) #s(literal 6 binary64))
(/.f64 (exp.f64 (log.f64 (*.f64 x (neg.f64 x)))) (exp.f64 (log.f64 #s(literal -6 binary64))))
(/.f64 (neg.f64 (neg.f64 (*.f64 x (neg.f64 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)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(.f64 (.f64 x #s(literal 1/6 binary64)) x)
(.f64 (neg.f64 x) (.f64 x #s(literal -1/6 binary64)))
(.f64 (neg.f64 x) (.f64 #s(literal -1/6 binary64) x))
(.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 (.f64 x #s(literal -1/6 binary64)) (neg.f64 x))
(.f64 (/.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1/6 binary64)))
(exp.f64 (log.f64 (*.f64 x #s(literal 1/6 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))))
(/.f64 x #s(literal 6 binary64))
(/.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) x))
(/.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))
(/.f64 #s(literal -1/6 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -6 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x))) #s(literal 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 (*.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))
(*.f64 #s(literal 1/6 binary64) x)
(.f64 (.f64 x #s(literal 1/6 binary64)) #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 #s(literal -1/6 binary64) (neg.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -1/6 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)))
#s(literal 1/6 binary64)
#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 (*.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64)))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal -1 binary64)))
(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 (*.f64 x x) (exp.f64 (log.f64 #s(literal 6 binary64))))
(/.f64 (*.f64 x #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) x))
(/.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) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 (log.f64 (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 6 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (*.f64 x (neg.f64 x)) #s(literal -6 binary64))
(/.f64 (neg.f64 (*.f64 x #s(literal 1/6 binary64))) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (*.f64 x (neg.f64 x))) #s(literal 6 binary64))
(/.f64 (exp.f64 (log.f64 (*.f64 x (neg.f64 x)))) (exp.f64 (log.f64 #s(literal -6 binary64))))
(/.f64 (neg.f64 (neg.f64 (*.f64 x (neg.f64 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)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(.f64 #s(literal 1/6 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1/6 binary64))
(.f64 (.f64 x #s(literal 1/6 binary64)) x)
(.f64 (neg.f64 x) (.f64 x #s(literal -1/6 binary64)))
(.f64 (neg.f64 x) (.f64 #s(literal -1/6 binary64) x))
(.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 (.f64 x #s(literal -1/6 binary64)) (neg.f64 x))
(.f64 (/.f64 x #s(literal 1 binary64)) (.f64 x #s(literal 1/6 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)))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 x) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (neg.f64 x) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(*.f64 x x)
(*.f64 (neg.f64 x) (neg.f64 x))
(+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64)))
(+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #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 x (*.f64 x #s(literal 1/6 binary64))) #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 x (.f64 x #s(literal 1/6 binary64))) #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 x) (.f64 x (.f64 x (.f64 x x)))) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64)))) #s(literal 6 binary64)) (/.f64 (/.f64 #s(literal 27 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 #s(literal 3 binary64) (*.f64 x x) #s(literal 9 binary64)))) #s(literal 6 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 x (.f64 x (*.f64 x 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 x) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64))))) (/.f64 #s(literal 27 binary64) (.f64 #s(literal 6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 #s(literal 3 binary64) (*.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 (.f64 x x))) (.f64 (.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 #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 x (.f64 x #s(literal 1/6 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) #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 #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (.f64 x #s(literal 1/6 binary64)) (/.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/6 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 (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (/.f64 (.f64 x (.f64 x #s(literal 1/6 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 (neg.f64 x) (*.f64 x #s(literal -1/6 binary64)) #s(literal -1/2 binary64))
(fma.f64 (neg.f64 x) (*.f64 #s(literal -1/6 binary64) x) #s(literal -1/2 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64)))) (/.f64 #s(literal 1 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 (.f64 x (.f64 x x))) (/.f64 #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 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal -1/2 binary64))
(fma.f64 (*.f64 x (neg.f64 x)) #s(literal -1/6 binary64) #s(literal -1/2 binary64))
(fma.f64 (.f64 (.f64 x x) #s(literal 1/36 binary64)) (/.f64 (.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 1/36 binary64) (/.f64 (.f64 x (.f64 x (.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 #s(literal -1/6 binary64)) (neg.f64 x) #s(literal -1/2 binary64))
(fma.f64 (.f64 x (.f64 (.f64 x x) #s(literal 1/36 binary64))) (/.f64 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 (.f64 x (.f64 x (.f64 x #s(literal 1/6 binary64))))) (/.f64 #s(literal 1/6 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 (.f64 x (.f64 x #s(literal 1/6 binary64)))) (/.f64 (.f64 x #s(literal 1/6 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 #s(literal 1 binary64)) (*.f64 x #s(literal 1/6 binary64)) #s(literal -1/2 binary64))
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(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.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 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x x) (.f64 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 x) (.f64 x (.f64 x (.f64 x x))))) #s(literal 1/1296 binary64))))
(.f64 (/.f64 (fma.f64 (.f64 (.f64 x x) (.f64 x (.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 (.f64 x x) (.f64 x (.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 x (*.f64 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 (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))) (.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 (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 x x) (.f64 (.f64 x x) (.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 x (.f64 x (.f64 x x)) (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (fma.f64 #s(literal 3 binary64) (.f64 x x) #s(literal 9 binary64))))
(.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))) (-.f64 (fma.f64 x (.f64 x (.f64 x x)) #s(literal 9 binary64)) (.f64 #s(literal 3 binary64) (.f64 x x))))
(exp.f64 (log.f64 (*.f64 x #s(literal 1/6 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))))
(/.f64 x #s(literal 6 binary64))
(/.f64 #s(literal 1/6 binary64) (/.f64 #s(literal 1 binary64) x))
(/.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))
(/.f64 #s(literal -1/6 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -6 binary64))
(/.f64 (neg.f64 (*.f64 #s(literal 1 binary64) (neg.f64 x))) #s(literal 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 (*.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))
(*.f64 #s(literal 1/6 binary64) x)
(.f64 (.f64 x #s(literal 1/6 binary64)) #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 #s(literal -1/6 binary64) (neg.f64 x))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 x)) #s(literal -1/6 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)))
(log.f64 #s(literal 1/6 binary64))

eval51.0ms (0.9%)

Memory: 35.4MiB live, 148.0MiB allocated
Compiler: Compiled 8 616 to 759 computations (91.2% saved)

prune44.0ms (0.8%)

Memory

-4.7MiB live, 112.0MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	458	1	459
Fresh	0	0	0
Picked	1	2	3
Done	0	5	5
Total	459	8	467

Accuracy

100.0%

Counts

467 → 8

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 #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	54.1%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	99.9%	(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
▶	54.1%	#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
✓	54.1%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	54.1%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))
✓	46.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 52 to 33 computations (36.5% saved)

simplify5.0ms (0.1%)

Memory

11.4MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 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))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
0	11	23
1	20	23
2	26	23
3	27	23
0	27	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#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 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)

localize46.0ms (0.9%)

Memory

-23.4MiB live, 69.6MiB allocated

Localize:

Found 3 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	54.2%	#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))

Samples

24.0ms

256×

valid

Compiler

Compiled 19 to 10 computations (47.4% saved)

Precisions

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

ival-div: 13.0ms (79% of total)

ival-mult: 2.0ms (12.2% of total)

ival-sub: 1.0ms (6.1% of total)

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

exact: 0.0ms (0% of total)

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

series1.0ms (0%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs
#<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 (* 1/6 (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

9 calls:

Time	Variable		Point	Expression
0.0ms	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))

simplify176.0ms (3.2%)

Memory

11.4MiB live, 270.5MiB allocated

Algorithm

1×	egg-herbie

Rules

3 338×	`lower-*.f64`
3 338×	`lower-*.f32`
2 710×	`lower-fma.f64`
2 710×	`lower-fma.f32`
1 528×	`div-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	170
1	29	170
2	60	170
3	137	170
4	369	170
5	703	170
6	1157	170
7	2174	170
8	3638	170
9	4728	170
10	5704	170
11	6870	170
0	8060	161

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

Inputs
(* 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
(* 1/6 (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)

rewrite320.0ms (5.9%)

Memory

-14.7MiB live, 448.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 590×	`lower-/.f32`
4 586×	`lower-/.f64`
4 020×	`lower-*.f64`
4 020×	`lower-*.f32`
2 762×	`lower-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
0	11	21
1	57	21
2	316	21
3	2550	21
0	8732	20

Stop Event

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

Counts

3 → 94

Calls

Call 1

Inputs
(/.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
(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 #s(literal -1/6 binary64) (.f64 x x)))
(-.f64 #s(literal 0 binary64) (/.f64 (*.f64 x x) #s(literal -6 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 6 binary64) x)) (.f64 #s(literal -1/6 binary64) (.f64 x x)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal -1 binary64) x)) (.f64 #s(literal -1/6 binary64) (.f64 x x)))
(-.f64 (/.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 6 binary64) x)) #s(literal 1 binary64)) (/.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)) #s(literal 1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal -1/6 binary64) (.f64 x x)))
(neg.f64 (.f64 #s(literal -1/6 binary64) (.f64 x x)))
(neg.f64 (/.f64 (*.f64 x x) #s(literal -6 binary64)))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(/.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 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(/.f64 (*.f64 x #s(literal 1/6 binary64)) (/.f64 #s(literal 1 binary64) 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 #s(literal -1/6 binary64) (.f64 x x)) #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 (.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 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 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 #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 (neg.f64 (neg.f64 (*.f64 x (neg.f64 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))
(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 (neg.f64 x) (.f64 x #s(literal -1/6 binary64)))
(.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 x (*.f64 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 #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 #s(literal -1/6 binary64) (*.f64 x x)))
(.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 (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))
(/.f64 #s(literal 6 binary64) x)
(/.f64 (/.f64 #s(literal 6 binary64) x) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal -6 binary64) x) #s(literal -1 binary64))
(/.f64 #s(literal -6 binary64) (neg.f64 x))
(/.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 #s(literal 6 binary64) x) #s(literal 1 binary64))
(pow.f64 (*.f64 x #s(literal 1/6 binary64)) #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)))

eval15.0ms (0.3%)

Memory: -3.2MiB live, 35.2MiB allocated
Compiler: Compiled 1 169 to 214 computations (81.7% saved)

prune18.0ms (0.3%)

Memory

-0.3MiB live, 41.8MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	130	8	138

Accuracy

100.0%

Counts

138 → 8

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 #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	54.1%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	99.9%	(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
✓	54.1%	#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
✓	54.1%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	54.1%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x #s(literal 1/6 binary64)) x))
✓	46.2%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 141 to 67 computations (52.5% saved)

regimes15.0ms (0.3%)

Memory

-1.0MiB live, 38.2MiB allocated

Counts

11 → 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)))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
#s(approx (/ (- (* x x) 3) 6) (/.f64 x (/.f64 #s(literal 6 binary64) x)))
(/.f64 (fma.f64 (.f64 x (.f64 x (.f64 x x))) (neg.f64 (.f64 x x)) #s(literal 27 binary64)) (.f64 #s(literal -6 binary64) (fma.f64 x (.f64 x (.f64 x x)) (fma.f64 (.f64 x x) #s(literal 3 binary64) #s(literal 9 binary64)))))
#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 x x) (exp.f64 (log.f64 #s(literal 1/6 binary64)))))

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

Calls

4 calls:

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

regimes11.0ms (0.2%)

Memory

-14.4MiB live, 24.4MiB allocated

Counts

6 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 20 to 13 computations (35% saved)

regimes7.0ms (0.1%)

Memory

16.1MiB live, 16.1MiB 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 x) #s(literal 1/6 binary64)))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
98.6%	2	`x`
98.6%	2	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
98.6%	2	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
98.6%	2	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

regimes6.0ms (0.1%)

Memory

15.2MiB live, 15.1MiB allocated

Counts

2 → 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))

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:

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

Results

Accuracy	Segments	Branch
98.6%	2	`x`
98.6%	2	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
98.6%	2	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
98.6%	2	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

regimes5.0ms (0.1%)

Memory

-26.6MiB live, 12.6MiB 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 x x)
1.0ms	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
46.2%	1	`x`
46.2%	1	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
46.2%	1	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
46.2%	1	`(*.f64 x x)`

Compiler

Compiled 20 to 13 computations (35% saved)

bsearch0.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.6622891700950695e-6	9.720898005331431

Compiler

Compiled 11 to 10 computations (9.1% saved)

bsearch0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.6622891700950695e-6	9.720898005331431

Compiler

Compiled 11 to 10 computations (9.1% saved)

simplify6.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	77
1	28	77

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(if (<=.f64 (.f64 x x) #s(literal 5902958103587057/1180591620717411303424 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))))
(if (<=.f64 (.f64 x x) #s(literal 5902958103587057/1180591620717411303424 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
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(*.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 1/6 binary64))
(if (<=.f64 (.f64 x x) #s(literal 5902958103587057/1180591620717411303424 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))))
(if (<=.f64 (.f64 x x) #s(literal 5902958103587057/1180591620717411303424 binary64)) #s(approx (/ (- ( x x) 3) 6) #s(literal -1/2 binary64)) #s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x))))
(if (<=.f64 (.f64 x x) #s(literal 5902958103587057/1180591620717411303424 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 5902958103587057/1180591620717411303424 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))

soundness624.0ms (11.5%)

Memory

-6.5MiB live, 354.8MiB allocated

Rules

6 244×	`lower-fma.f32`
6 240×	`lower-fma.f64`
6 230×	`lower-*.f32`
6 222×	`lower-*.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	6	15
0	9	15
1	42	15
2	230	15
3	1831	15
0	8685	13
0	19	69
0	27	65
1	95	65
2	512	65
3	4241	65
0	10225	65

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 109 to 63 computations (42.2% saved)

preprocess32.0ms (0.6%)

Memory: -8.4MiB live, 68.3MiB allocated
Remove: (abs x)
Compiler: Compiled 116 to 56 computations (51.7% 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%)

sample953.0ms (17.5%)

preprocess23.0ms (0.4%)

explain80.0ms (1.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify11.0ms (0.2%)

localize56.0ms (1%)

series2.0ms (0%)

simplify206.0ms (3.8%)

rewrite488.0ms (9%)

eval70.0ms (1.3%)

prune67.0ms (1.2%)

simplify6.0ms (0.1%)

localize50.0ms (0.9%)

series5.0ms (0.1%)

simplify285.0ms (5.2%)

rewrite936.0ms (17.2%)

eval102.0ms (1.9%)

prune77.0ms (1.4%)

simplify8.0ms (0.2%)

localize86.0ms (1.6%)

series34.0ms (0.6%)

simplify197.0ms (3.6%)

rewrite314.0ms (5.8%)

eval51.0ms (0.9%)

prune44.0ms (0.8%)

simplify5.0ms (0.1%)

localize46.0ms (0.9%)

series1.0ms (0%)

simplify176.0ms (3.2%)

rewrite320.0ms (5.9%)

eval15.0ms (0.3%)

prune18.0ms (0.3%)

regimes15.0ms (0.3%)

regimes11.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

soundness624.0ms (11.5%)

preprocess32.0ms (0.6%)

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