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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze0.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample825.0ms (21.1%)

Memory

45.7MiB live, 902.1MiB allocated

Samples

412.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 237.0ms

ival-mult: 122.0ms (51.4% of total)

ival-div: 57.0ms (24% of total)

ival-sub: 40.0ms (16.9% of total)

exact: 9.0ms (3.8% of total)

ival-true: 6.0ms (2.5% of total)

ival-assert: 3.0ms (1.3% of total)

Bogosity

explain205.0ms (5.3%)

Memory

-6.7MiB live, 74.9MiB 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

124.0ms

512×

valid

Compiler

Compiled 47 to 22 computations (53.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 113.0ms

ival-mult: 106.0ms (94% of total)

ival-sub: 3.0ms (2.7% of total)

ival-div: 3.0ms (2.7% of total)

exact: 1.0ms (0.9% of total)

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

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

preprocess98.0ms (2.5%)

Memory

-26.3MiB live, 12.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 7 to 6 computations (14.3% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 1 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

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

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0.1%)

Memory

1.6MiB live, 1.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize16.0ms (0.4%)

Memory

12.4MiB live, 12.4MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(-.f64 (*.f64 x x) #s(literal 3 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.0703125	(/.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 (37.1% of total)

ival-mult: 2.0ms (37.1% of total)

ival-sub: 1.0ms (18.5% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

2.3MiB live, 2.3MiB allocated

Counts

3 → 36

Calls

Call 1

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

Inputs

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

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

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

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

Calls

3 calls:

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

simplify251.0ms (6.4%)

Memory

-13.1MiB live, 74.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

Calls

Call 1

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

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

rewrite234.0ms (6%)

Memory

19.1MiB live, 244.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

3 → 516

Calls

Call 1

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

Outputs
#<batchref>
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eval83.0ms (2.1%)

Memory: -0.5MiB live, 152.5MiB allocated
Compiler: Compiled 14 583 to 1 649 computations (88.7% saved)

prune14.0ms (0.4%)

Memory

11.3MiB live, 49.8MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

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

Accuracy

100.0%

Counts

553 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
▶	99.9%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
▶	99.9%	(/.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 6 binary64))
	62.5%	(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64)))
	53.3%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	53.3%	#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
▶	47.0%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 88 to 76 computations (13.6% saved)

simplify4.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	70
0	27	68
1	40	68
2	44	68
3	46	68
0	46	68

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

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

localize46.0ms (1.2%)

Memory

-22.8MiB live, 104.6MiB allocated

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.08203125	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
accuracy	0.05859375	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
accuracy	0.375	(*.f64 x #s(literal 1/6 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.16796875	(.f64 #s(literal 1/6 binary64) (.f64 x x))
accuracy	29.84544343330507	#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
accuracy	33.917704739966226	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))
accuracy	0	(fma.f64 x x #s(literal -3 binary64))
accuracy	0.0703125	(/.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 6 binary64))

Samples

34.0ms

256×

valid

Compiler

Compiled 68 to 19 computations (72.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 8.0ms (34.1% of total)

ival-div: 5.0ms (21.3% of total)

ival-add: 5.0ms (21.3% of total)

const: 4.0ms (17.1% of total)

ival-sub: 1.0ms (4.3% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.2%)

Memory

14.9MiB live, 14.9MiB allocated

Counts

9 → 108

Calls

Call 1

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

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

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((/ (+ (* x x) -3) 6) (+ (* x x) -3) (/ (- (* x x) 3) 6) (/ (- (* x x) 3) 6) (* 1/6 (* x x)) (* x x) (+ (* (* x 1/6) x) -1/2) (* x 1/6) (+ (* (* x x) 1/6) -1/2))
1.0ms	x	@	inf	((/ (+ (* x x) -3) 6) (+ (* x x) -3) (/ (- (* x x) 3) 6) (/ (- (* x x) 3) 6) (* 1/6 (* x x)) (* x x) (+ (* (* x 1/6) x) -1/2) (* x 1/6) (+ (* (* x x) 1/6) -1/2))
1.0ms	x	@	-inf	((/ (+ (* x x) -3) 6) (+ (* x x) -3) (/ (- (* x x) 3) 6) (/ (- (* x x) 3) 6) (* 1/6 (* x x)) (* x x) (+ (* (* x 1/6) x) -1/2) (* x 1/6) (+ (* (* x x) 1/6) -1/2))

Time

Variable

Point

Expression

1.0ms

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

1.0ms

inf

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

1.0ms

-inf

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

simplify145.0ms (3.7%)

Memory

-10.2MiB live, 122.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	554
1	45	554
2	98	554
3	232	554
4	740	554
5	1580	554
6	2324	554
7	3496	554
8	4216	554
9	5320	554
10	6373	554
11	7104	554
0	8017	500

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

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

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

rewrite182.0ms (4.7%)

Memory

-16.9MiB live, 334.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	55
0	27	53
1	107	53
2	499	53
3	4078	53
0	9957	53

Stop Event

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

Counts

9 → 730

Calls

Call 1

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

Outputs
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eval90.0ms (2.3%)

Memory: 22.3MiB live, 174.9MiB allocated
Compiler: Compiled 13 763 to 944 computations (93.1% saved)

prune20.0ms (0.5%)

Memory

18.7MiB live, 55.7MiB allocated

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	854	2	856
Fresh	1	1	2
Picked	1	4	5
Done	0	0	0
Total	856	7	863

Accuracy

100.0%

Counts

863 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
✓	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	99.9%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
▶	53.3%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	53.2%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 #s(literal 1/6 binary64) x) x))
✓	53.3%	#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
✓	47.0%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 38 to 33 computations (13.2% saved)

simplify4.0ms (0.1%)

Memory

3.3MiB live, 3.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 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	#s(approx (- (* x x) 3) (*.f64 x x))
cost-diff	0	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
cost-diff	0	(*.f64 #s(literal 1/6 binary64) x)
cost-diff	0	(.f64 (.f64 #s(literal 1/6 binary64) x) x)
cost-diff	0	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 #s(literal 1/6 binary64) x) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	60
0	23	60
1	36	59
2	39	59
0	39	57

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

localize59.0ms (1.5%)

Memory

-46.6MiB live, 87.5MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x #s(literal 6 binary64))
accuracy	0.05859375	(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
accuracy	0	(*.f64 x x)
accuracy	0.0703125	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
accuracy	29.846897363632795	#s(approx (- (* x x) 3) (*.f64 x x))
accuracy	0.12890625	(.f64 (.f64 #s(literal 1/6 binary64) x) x)
accuracy	0.375	(*.f64 #s(literal 1/6 binary64) x)
accuracy	29.84544343330507	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 #s(literal 1/6 binary64) x) x))

Samples

46.0ms

256×

valid

Compiler

Compiled 49 to 15 computations (69.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 23.0ms (70.4% of total)

const: 4.0ms (12.2% of total)

ival-div: 3.0ms (9.2% of total)

ival-sub: 1.0ms (3.1% of total)

ival-add: 1.0ms (3.1% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

11.8MiB live, 11.8MiB allocated

Counts

8 → 96

Calls

Call 1

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

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

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

1.0ms

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

simplify112.0ms (2.9%)

Memory

19.5MiB live, 100.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	442
1	45	442
2	98	442
3	232	442
4	736	442
5	1574	442
6	2320	442
7	3494	442
8	4218	442
9	5325	442
10	6379	442
11	7108	442
0	8021	406

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

rewrite150.0ms (3.8%)

Memory

-20.5MiB live, 209.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	53
0	23	53
1	85	52
2	444	52
3	4170	52
0	8954	50

Stop Event

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

Counts

8 → 334

Calls

Call 1

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

Outputs
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eval49.0ms (1.3%)

Memory: 0.6MiB live, 82.5MiB allocated
Compiler: Compiled 6 175 to 878 computations (85.8% saved)

prune13.0ms (0.3%)

Memory

-8.5MiB live, 30.3MiB allocated

Pruning

8 alts after pruning (1 fresh and 7 done)

	Pruned	Kept	Total
New	429	1	430
Fresh	0	0	0
Picked	0	3	3
Done	0	4	4
Total	429	8	437

Accuracy

100.0%

Counts

437 → 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))
✓	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	99.9%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	53.3%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
▶	53.3%	#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))
✓	53.2%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 #s(literal 1/6 binary64) x) x))
✓	53.3%	#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
✓	47.0%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 44 to 38 computations (13.6% saved)

simplify3.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
0	11	23
1	20	23
2	24	23
3	25	23
0	25	22

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize19.0ms (0.5%)

Memory

31.6MiB live, 31.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(/.f64 x #s(literal 6 binary64))
accuracy	0.12890625	(*.f64 (/.f64 x #s(literal 6 binary64)) x)
accuracy	29.84544343330507	#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))

Samples

14.0ms

256×

valid

Compiler

Compiled 19 to 10 computations (47.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-div: 3.0ms (36.3% of total)

ival-mult: 3.0ms (36.3% of total)

ival-sub: 1.0ms (12.1% of total)

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

exact: 0.0ms (0% of total)

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

series5.0ms (0.1%)

Memory

-32.6MiB live, 6.2MiB allocated

Counts

3 → 36

Calls

Call 1

Inputs

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

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

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

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

Calls

3 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	((/ (- (* x x) 3) 6) (* (/ x 6) x) (/ x 6))
1.0ms	x	@	inf	((/ (- (* x x) 3) 6) (* (/ x 6) x) (/ x 6))
1.0ms	x	@	0	((/ (- (* x x) 3) 6) (* (/ x 6) x) (/ x 6))

simplify165.0ms (4.2%)

Memory

8.7MiB live, 91.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	170
1	29	170
2	58	170
3	132	170
4	362	170
5	698	170
6	1153	170
7	2165	170
8	3613	170
9	4693	170
10	5638	170
11	6785	170
12	7934	170
0	8469	161

Stop Event

1×	iter limit
1×	node limit

Counts

36 → 36

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

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

rewrite171.0ms (4.4%)

Memory

7.9MiB live, 117.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	21
0	11	21
1	51	21
2	265	21
3	2111	21
0	9117	20

Stop Event

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

Counts

3 → 98

Calls

Call 1

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

Outputs
#<batchref>
#<batchref>
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#<batchref>
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#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
#<batchref>
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#<batchref>
#<batchref>

eval13.0ms (0.3%)

Memory: 19.5MiB live, 19.5MiB allocated
Compiler: Compiled 1 137 to 313 computations (72.5% saved)

prune44.0ms (1.1%)

Memory

-18.0MiB live, 28.7MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	0	0
Picked	0	1	1
Done	0	7	7
Total	134	8	142

Accuracy

100.0%

Counts

142 → 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))
✓	99.9%	(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
✓	99.9%	(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
✓	53.3%	(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
✓	53.3%	#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))
✓	53.2%	#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 #s(literal 1/6 binary64) x) x))
✓	53.3%	#s(approx (/ (- (* x x) 3) 6) (.f64 #s(literal 1/6 binary64) (.f64 x x)))
✓	47.0%	#s(approx (/ (- (* x x) 3) 6) #s(literal -1/2 binary64))

Compiler

Compiled 113 to 71 computations (37.2% saved)

regimes43.0ms (1.1%)

Memory

-16.6MiB live, 22.1MiB 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 #s(literal 1/6 binary64) (.f64 x x)))
#s(approx (/ (- (* x x) 3) 6) (.f64 (.f64 #s(literal 1/6 binary64) x) x))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal -1/2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal -1/2 binary64))
#s(approx (/ (- (* x x) 3) 6) (*.f64 (/.f64 x #s(literal 6 binary64)) x))
(/.f64 #s(approx (- (* x x) 3) (*.f64 x x)) #s(literal 6 binary64))
(/.f64 (fma.f64 x x #s(literal -3 binary64)) #s(literal 6 binary64))
(fma.f64 (/.f64 x #s(literal 6 binary64)) x #s(literal -1/2 binary64))
(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal 9 binary64)) (*.f64 (fma.f64 x x #s(literal 3 binary64)) #s(literal 6 binary64)))

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

Calls

4 calls:

33.0ms	x
3.0ms	(*.f64 x x)
3.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
3.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes11.0ms (0.3%)

Memory

13.8MiB live, 13.8MiB allocated

Counts

8 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes11.0ms (0.3%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes8.0ms (0.2%)

Memory

10.4MiB live, 10.4MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes21.0ms (0.5%)

Memory

-29.2MiB live, 9.6MiB allocated

Counts

3 → 2

Calls

Call 1

Inputs

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

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

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

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

Calls

4 calls:

16.0ms	(*.f64 x x)
2.0ms	x
2.0ms	(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))
2.0ms	(-.f64 (*.f64 x x) #s(literal 3 binary64))

Results

Accuracy	Segments	Branch
98.5%	2	`x`
98.5%	2	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
98.5%	2	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
98.5%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

regimes5.0ms (0.1%)

Memory

7.7MiB live, 7.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
47.0%	1	`x`
47.0%	1	`(/.f64 (-.f64 (*.f64 x x) #s(literal 3 binary64)) #s(literal 6 binary64))`
47.0%	1	`(-.f64 (*.f64 x x) #s(literal 3 binary64))`
47.0%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 13 computations (18.8% saved)

bsearch0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.8818876715182359	576320411.2646981

Compiler

Compiled 10 to 10 computations (0% saved)

simplify31.0ms (0.8%)

Memory

-8.0MiB live, 31.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	61
1	28	61

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

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

soundness671.0ms (17.2%)

Memory

28.5MiB live, 294.0MiB allocated

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
0	18	55
0	27	53
1	107	53
2	499	53
3	4078	53
0	9957	53
0	19	162
1	43	162
2	98	162
3	236	162
4	759	162
5	1590	162
6	2334	162
7	3514	162
8	4236	162
9	5345	162
10	6402	162
11	7126	162
0	8039	144

Stop Event

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

Compiler

Compiled 111 to 73 computations (34.2% saved)

preprocess66.0ms (1.7%)

Memory: -14.3MiB live, 99.8MiB allocated
Remove: (abs x)
Compiler: Compiled 118 to 70 computations (40.7% 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

start0.0ms (0%)

analyze0.0ms (0%)

sample825.0ms (21.1%)

explain205.0ms (5.3%)

preprocess98.0ms (2.5%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize16.0ms (0.4%)

series3.0ms (0.1%)

simplify251.0ms (6.4%)

rewrite234.0ms (6%)

eval83.0ms (2.1%)

prune14.0ms (0.4%)

simplify4.0ms (0.1%)

localize46.0ms (1.2%)

series6.0ms (0.2%)

simplify145.0ms (3.7%)

rewrite182.0ms (4.7%)

eval90.0ms (2.3%)

prune20.0ms (0.5%)

simplify4.0ms (0.1%)

localize59.0ms (1.5%)

series5.0ms (0.1%)

simplify112.0ms (2.9%)

rewrite150.0ms (3.8%)

eval49.0ms (1.3%)

prune13.0ms (0.3%)

simplify3.0ms (0.1%)

localize19.0ms (0.5%)

series5.0ms (0.1%)

simplify165.0ms (4.2%)

rewrite171.0ms (4.4%)

eval13.0ms (0.3%)

prune44.0ms (1.1%)

regimes43.0ms (1.1%)

regimes11.0ms (0.3%)

regimes11.0ms (0.3%)

regimes8.0ms (0.2%)

regimes21.0ms (0.5%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

simplify31.0ms (0.8%)

soundness671.0ms (17.2%)

preprocess66.0ms (1.7%)

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