Metrics for cos2 (problem 3.4.1)

analyze4.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
75%	75%	25%	0%	0%	0%	0%	3
87.5%	87.5%	12.5%	0%	0%	0%	0%	4
93.8%	93.7%	6.2%	0%	0%	0%	0%	5
96.9%	96.8%	3.1%	0%	0%	0%	0%	6
98.4%	98.4%	1.6%	0%	0%	0%	0%	7
99.2%	99.2%	0.8%	0%	0%	0%	0%	8
99.6%	99.6%	0.4%	0%	0%	0%	0%	9
99.8%	99.8%	0.2%	0%	0%	0%	0%	10
99.9%	99.9%	0.1%	0%	0%	0%	0%	11
100%	99.9%	0%	0%	0%	0%	0%	12

Compiler

Compiled 10 to 7 computations (30% saved)

Precisions

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

ival-cos: 1.0ms (58.3% of total)

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

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

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

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample3.1s (15.9%)

Results

1.3s	2001×	2	valid
690.0ms	4174×	0	valid
580.0ms	2081×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 2.1s

ival-cos: 1.2s (58.4% of total)

ival-div: 281.0ms (13.4% of total)

ival-mult: 246.0ms (11.7% of total)

ival-sub: 191.0ms (9.1% of total)

backward-pass: 128.0ms (6.1% of total)

const: 28.0ms (1.3% of total)

Bogosity

preprocess234.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

1096×	`fnmadd-define`
1018×	`sum3-define`
1016×	`fma-define`
936×	`sum5-define`
904×	`sum3-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	38	25
2	111	24
3	309	24
4	835	24
5	1930	24
6	3633	24
7	3842	24
0	6	8
1	15	8
2	27	8
3	45	8
4	84	8
5	144	8
6	235	8
7	463	8
8	1139	8
9	2518	8
10	4027	8
11	4047	8
0	4047	8

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(/ (- 1 (cos x)) (* x x))

Outputs
(/ (- 1 (cos x)) (* x x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Call 2

Inputs
(/ (- 1 (cos x)) (* x x))
(/ (- 1 (cos (neg x))) (* (neg x) (neg x)))
(neg (/ (- 1 (cos (neg x))) (* (neg x) (neg x))))

Outputs
(/ (- 1 (cos x)) (* x x))
(/ (- 1 (cos (neg x))) (* (neg x) (neg x)))
(/ (- 1 (cos x)) (* x x))
(neg (/ (- 1 (cos (neg x))) (* (neg x) (neg x))))
(/ (+ (cos x) -1) (* x x))

Symmetry

(abs x)

explain273.0ms (1.4%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
71	2	(5.5488769520512e-162)	1	(1.7924708875397926e+191)	`(-.f64 #s(literal 1 binary64) (cos.f64 x))`
61	0	-	1	(1.0068677766568569e-161)	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`
0	0	-	0	-	`x`
0	0	-	0	-	`(*.f64 x x)`
0	0	-	0	-	`#s(literal 1 binary64)`
0	0	-	0	-	`(cos.f64 x)`

Results

96.0ms	124×	2	valid
62.0ms	266×	0	valid
47.0ms	122×	1	valid

Compiler

Compiled 51 to 20 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-cos: 82.0ms (60.2% of total)

ival-mult: 14.0ms (10.3% of total)

ival-sub: 14.0ms (10.3% of total)

ival-div: 13.0ms (9.5% of total)

backward-pass: 11.0ms (8.1% of total)

const: 2.0ms (1.5% of total)

eval1.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 9 to 6 computations (33.3% saved)

simplify144.0ms (0.7%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(cos.f64 x)
✓	cost-diff	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Rules

1096×	`fnmadd-define`
1018×	`sum3-define`
1016×	`fma-define`
880×	`sum5-define`
550×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	15	19
2	27	19
3	45	19
4	84	19
5	144	19
6	235	19
7	463	19
8	1139	19
9	2518	19
10	4027	19
11	4047	19
0	4047	19

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(/ (- 1 (cos x)) (* x x))
(- 1 (cos x))
1
(cos x)
x
(* x x)

Outputs
(/ (- 1 (cos x)) (* x x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(cos x)
(cos.f64 x)
x
(* x x)
(*.f64 x x)

localize206.0ms (1.1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	77.3%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	77.1%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Results

48.0ms	62×	2	valid
30.0ms	133×	0	valid
24.0ms	61×	1	valid

Compiler

Compiled 21 to 7 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-cos: 40.0ms (58.3% of total)

ival-div: 9.0ms (13.1% of total)

ival-mult: 7.0ms (10.2% of total)

backward-pass: 6.0ms (8.7% of total)

ival-sub: 6.0ms (8.7% of total)

const: 1.0ms (1.5% of total)

series7.0ms (0%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (/ (- 1 (cos x)) (* x x))>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (* x x)>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ (- 1 (cos x)) (* x x))
1.0ms	x	@	inf	(* x x)
1.0ms	x	@	-inf	(/ (- 1 (cos x)) (* x x))
1.0ms	x	@	0	(/ (- 1 (cos x)) (* x x))
0.0ms	x	@	0	(cos x)

rewrite710.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2600×	`-lowering-.f32`
2600×	`-lowering-.f64`
2226×	`fma-lowering-fma.f32`
2226×	`fma-lowering-fma.f64`
1948×	`prod-diff`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	17
1	36	17
2	268	17
3	2905	17
0	8648	17

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 462

Calls

Call 1

Inputs
(/ (- 1 (cos x)) (* x x))
(- 1 (cos x))
(cos x)
(* x x)

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

simplify475.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2236×	`sum3-define`
2048×	`fma-lowering-fma.f32`
2048×	`fma-lowering-fma.f64`
1796×	`sum4-define`
1588×	`fmsub-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	42	278
1	113	266
2	315	266
3	818	266
4	1931	266
5	2941	266
6	3513	266
7	4835	266
0	8655	266

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))))))
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(/ (- 1 (cos x)) (pow x 2))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(* 1/2 (pow x 2))
(.f64 #s(literal 1/2 binary64) (.f64 x x))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 x (.f64 x #s(literal -1/40320 binary64))))))))))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(+ 1 (* -1/2 (pow x 2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (-.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/24 binary64) (.f64 (.f64 x x) #s(literal -1/720 binary64))))))))
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(cos x)
(cos.f64 x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval210.0ms (1.1%)

Compiler: Compiled 13161 to 1210 computations (90.8% saved)

prune177.0ms (0.9%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	492	18	510
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	492	19	511

Accuracy

100.0%

Counts

511 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	52.2%	(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 x x)))
	51.8%	(/.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
	29.5%	(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
	51.8%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
▶	53.5%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
▶	17.3%	(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 x))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
	45.5%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	52.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	24.9%	(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
	51.8%	(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
	52.3%	(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
▶	52.2%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
	52.3%	(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
	49.7%	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
	49.2%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
▶	76.0%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	52.3%	(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
	53.5%	(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x))
▶	50.3%	#s(literal 1/2 binary64)

Compiler

Compiled 503 to 298 computations (40.8% saved)

simplify330.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (*.f64 x x))
✓	cost-diff	384	(-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (cos.f64 x)))
✓	cost-diff	1024	(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 x))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
✓	cost-diff	0	(/.f64 (cos.f64 x) (*.f64 x x))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	256	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	cost-diff	0	(cos.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
✓	cost-diff	0	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	0	(/.f64 (sin.f64 x) (*.f64 x x))
✓	cost-diff	0	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Rules

1688×	`fnmadd-define`
1466×	`-lowering-.f32`
1466×	`-lowering-.f64`
1260×	`fma-lowering-fma.f32`
1260×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	23	125
1	62	122
2	181	121
3	826	119
4	4167	116
0	8232	116

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (/ (sin x) (* x x)) (tan (/ x 2)))
(/ (sin x) (* x x))
(sin x)
x
(* x x)
(tan (/ x 2))
(/ x 2)
2
1/2
(/ (/ (- 1 (cos x)) x) x)
(/ (- 1 (cos x)) x)
(- 1 (cos x))
1
(cos x)
x
(- (/ 1 (* x x)) (/ (cos x) (* x x)))
(/ 1 (* x x))
1
(* x x)
x
(/ (cos x) (* x x))
(cos x)
(/ (- (- 0 (* x x)) (* (- 0 (* x x)) (cos x))) (* (- 0 (* x x)) (* x x)))
(- (- 0 (* x x)) (* (- 0 (* x x)) (cos x)))
(- 0 (* x x))
0
(* x x)
x
(* (- 0 (* x x)) (cos x))
(cos x)
(* (- 0 (* x x)) (* x x))

Outputs
(* (/ (sin x) (* x x)) (tan (/ x 2)))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/ (sin x) (* x x))
(/.f64 (/.f64 (sin.f64 x) x) x)
(sin x)
(sin.f64 x)
x
(* x x)
(*.f64 x x)
(tan (/ x 2))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
1/2
#s(literal 1/2 binary64)
(/ (/ (- 1 (cos x)) x) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ (- 1 (cos x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
1
#s(literal 1 binary64)
(cos x)
(cos.f64 x)
x
(- (/ 1 (* x x)) (/ (cos x) (* x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ 1 (* x x))
(/.f64 #s(literal 1 binary64) (*.f64 x x))
1
#s(literal 1 binary64)
(* x x)
(*.f64 x x)
x
(/ (cos x) (* x x))
(/.f64 (/.f64 (cos.f64 x) x) x)
(cos x)
(cos.f64 x)
(/ (- (- 0 (* x x)) (* (- 0 (* x x)) (cos x))) (* (- 0 (* x x)) (* x x)))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(- (- 0 (* x x)) (* (- 0 (* x x)) (cos x)))
(.f64 x (.f64 x (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(- 0 (* x x))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
0
#s(literal 0 binary64)
(* x x)
(*.f64 x x)
x
(* (- 0 (* x x)) (cos x))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(cos x)
(cos.f64 x)
(* (- 0 (* x x)) (* x x))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))

localize514.0ms (2.7%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 x))
✓	accuracy	99.8%	(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))
✓	accuracy	77.4%	(-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x)) (cos.f64 x)))
✓	accuracy	30.2%	(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 x))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	99.4%	(/.f64 (cos.f64 x) (*.f64 x x))
✓	accuracy	53.5%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
✓	accuracy	77.5%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
✓	accuracy	77.3%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	100.0%	(sin.f64 x)
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.7%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	accuracy	77.1%	(/.f64 (sin.f64 x) (*.f64 x x))

Results

143.0ms	61×	2	valid
107.0ms	133×	0	valid
88.0ms	37×	1	valid
83.0ms	25×	3	valid

Compiler

Compiled 153 to 24 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 229.0ms

ival-div: 63.0ms (27.5% of total)

ival-cos: 48.0ms (21% of total)

ival-mult: 34.0ms (14.9% of total)

backward-pass: 28.0ms (12.2% of total)

ival-sub: 23.0ms (10.1% of total)

ival-sin: 17.0ms (7.4% of total)

ival-tan: 13.0ms (5.7% of total)

const: 2.0ms (0.9% of total)

series35.0ms (0.2%)

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (* (/ (sin x) (* x x)) (tan (/ x 2)))>
#<alt (/ (sin x) (* x x))>
#<alt (sin x)>
#<alt (* x x)>
#<alt (/ (/ (- 1 (cos x)) x) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (- 1 (cos x))>
#<alt (cos x)>
#<alt (- (/ 1 (* x x)) (/ (cos x) (* x x)))>
#<alt (/ 1 (* x x))>
#<alt (/ (cos x) (* x x))>
#<alt (/ (- (- 0 (* x x)) (* (- 0 (* x x)) (cos x))) (* (- 0 (* x x)) (* x x)))>
#<alt (- (- 0 (* x x)) (* (- 0 (* x x)) (cos x)))>
#<alt (- 0 (* x x))>
#<alt (tan (/ x 2))>
#<alt (* (- 0 (* x x)) (* x x))>
#<alt (* (- 0 (* x x)) (cos x))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/6 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (pow x 2))>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt (/ (cos x) (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (* -1/2 (pow x 4))>
#<alt (* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))>
#<alt (* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))>
#<alt (* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (pow x 2)) 1))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1))>
#<alt (* (pow x 2) (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))>
#<alt (* -1 (* (pow x 2) (cos x)))>
#<alt (* -1 (* (pow x 2) (cos x)))>
#<alt (* -1 (* (pow x 2) (cos x)))>
#<alt (* -1 (* (pow x 2) (cos x)))>
#<alt (* -1 (* (pow x 2) (cos x)))>
#<alt (* -1 (* (pow x 2) (cos x)))>
#<alt (* -1 (* (pow x 2) (cos x)))>
#<alt (* -1 (* (pow x 2) (cos x)))>

Calls

51 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
4.0ms	x	@	-inf	(- (/ 1 (* x x)) (/ (cos x) (* x x)))
4.0ms	x	@	inf	(* (/ (sin x) (* x x)) (tan (/ x 2)))
3.0ms	x	@	inf	(/ (- (- 0 (* x x)) (* (- 0 (* x x)) (cos x))) (* (- 0 (* x x)) (* x x)))
2.0ms	x	@	-inf	(/ (- (- 0 (* x x)) (* (- 0 (* x x)) (cos x))) (* (- 0 (* x x)) (* x x)))

rewrite1000.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3404×	`/-lowering-/.f32`
3404×	`/-lowering-/.f64`
2164×	`-lowering-.f32`
2164×	`-lowering-.f64`
1252×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	102
1	162	94
2	1666	91
0	9177	91

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 1560

Calls

Call 1

Inputs
(* (/ (sin x) (* x x)) (tan (/ x 2)))
(/ (sin x) (* x x))
(sin x)
(* x x)
(/ (/ (- 1 (cos x)) x) x)
(/ (- 1 (cos x)) x)
(- 1 (cos x))
(cos x)
(- (/ 1 (* x x)) (/ (cos x) (* x x)))
(/ 1 (* x x))
(/ (cos x) (* x x))
(/ (- (- 0 (* x x)) (* (- 0 (* x x)) (cos x))) (* (- 0 (* x x)) (* x x)))
(- (- 0 (* x x)) (* (- 0 (* x x)) (cos x)))
(- 0 (* x x))
(tan (/ x 2))
(* (- 0 (* x x)) (* x x))
(* (- 0 (* x x)) (cos x))

Outputs
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 (.f64 x x) (sin.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (cos.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (/.f64 (sin.f64 x) x) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (.f64 x x) (sin.f64 x))) (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)) (*.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) x) (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (sin.f64 x)) (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x)))
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(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (*.f64 x x))))))
(.f64 (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 0 binary64))))))
(.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (+.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))))))
(.f64 (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (-.f64 #s(literal 0 binary64) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (pow.f64 (.f64 #s(literal 1 binary64) x) #s(literal 2 binary64)) (*.f64 x x))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64)) (.f64 x x))
(+.f64 (.f64 (cos.f64 x) #s(literal 0 binary64)) (.f64 x (*.f64 x (cos.f64 x))))
(+.f64 (.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x (*.f64 x (cos.f64 x))))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (cos.f64 x))))
(fma.f64 (cos.f64 x) #s(literal 0 binary64) (.f64 x (.f64 x (cos.f64 x))))
(fma.f64 #s(literal 0 binary64) (cos.f64 x) (.f64 x (.f64 x (cos.f64 x))))
(neg.f64 (.f64 x (.f64 x (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (cos.f64 x) (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (cos.f64 x) (.f64 x (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (*.f64 x x)))) (cos.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (*.f64 x (cos.f64 x))))))
(/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (*.f64 x x))
(/.f64 (.f64 (cos.f64 x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (.f64 (cos.f64 x) (.f64 x (.f64 x (.f64 x x)))) (*.f64 x x))
(/.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (cos.f64 x)) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (cos.f64 x) (.f64 x (.f64 x (.f64 x x))))) (*.f64 x x))
(/.f64 (neg.f64 (.f64 (cos.f64 x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (cos.f64 x))) (.f64 x (.f64 x (*.f64 x x))))
(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 x) #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 x (cos.f64 x))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 (cos.f64 x) #s(literal 0 binary64)) (.f64 (cos.f64 x) #s(literal 0 binary64))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 (cos.f64 x) #s(literal 0 binary64)) (.f64 x (.f64 x (cos.f64 x)))))))
(/.f64 (+.f64 (pow.f64 (.f64 #s(literal 0 binary64) (cos.f64 x)) #s(literal 3 binary64)) (pow.f64 (.f64 x (.f64 x (cos.f64 x))) #s(literal 3 binary64))) (+.f64 (.f64 (.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 #s(literal 0 binary64) (cos.f64 x))) (-.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 (.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x (.f64 x (cos.f64 x)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 x (.f64 x (cos.f64 x))) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 #s(literal 0 binary64) (.f64 x (*.f64 x (cos.f64 x)))))))
(.f64 x (.f64 x (cos.f64 x)))
(.f64 (.f64 x x) (cos.f64 x))
(.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) (cos.f64 x)))
(.f64 (cos.f64 x) (.f64 x x))
(.f64 #s(literal -1 binary64) (.f64 x (*.f64 x (cos.f64 x))))
(.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (.f64 x x))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 (cos.f64 x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))
(.f64 (.f64 (cos.f64 x) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (cos.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))))

simplify900.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

3798×	`-lowering-.f32`
3798×	`-lowering-.f64`
3024×	`+-lowering-+.f64`
3024×	`+-lowering-+.f32`
1432×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	128	1491
1	364	1441
2	1036	1432
3	3548	1421
4	6557	1413
0	8023	1413

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ 1 x)
(/ (+ 1 (* -1/6 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ (+ 1 (* -1/2 (pow x 2))) (pow x 2))
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) (pow x 2))
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
(/ (cos x) (pow x 2))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* -1/2 (pow x 4))
(* (pow x 4) (- (* 1/24 (pow x 2)) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 2))
(* (pow x 2) (- (* 1/2 (pow x 2)) 1))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))
(* -1 (* (pow x 2) (cos x)))
(* -1 (* (pow x 2) (cos x)))
(* -1 (* (pow x 2) (cos x)))
(* -1 (* (pow x 2) (cos x)))
(* -1 (* (pow x 2) (cos x)))
(* -1 (* (pow x 2) (cos x)))
(* -1 (* (pow x 2) (cos x)))
(* -1 (* (pow x 2) (cos x)))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 #s(literal 1/2 binary64) x))) (.f64 (.f64 x x) (cos.f64 (*.f64 #s(literal 1/2 binary64) x))))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ (+ 1 (* -1/6 (pow x 2))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/6 binary64))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal -1/5040 binary64)))))))) x)
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
(/ (sin x) (pow x 2))
(/.f64 (sin.f64 x) (*.f64 x x))
x
(* x (+ 1 (* -1/6 (pow x 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (*.f64 x x) #s(literal -1/6 binary64))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/6 binary64) (.f64 x (*.f64 x #s(literal 1/120 binary64)))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (*.f64 x x) #s(literal -1/5040 binary64)))))))))
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(sin x)
(sin.f64 x)
(pow x 2)
(*.f64 x x)
(pow x 2)
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#s(literal 1/2 binary64)
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1/2
#s(literal 1/2 binary64)
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(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))
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(* (pow x 4) (- (* (pow x 2) (+ 1/24 (* (pow x 2) (- (* 1/40320 (pow x 2)) 1/720)))) 1/2))
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(* -1 (* (pow x 2) (+ 1 (* -1 (cos x)))))
(.f64 (.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
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(* 1/2 x)
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(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (*.f64 x #s(literal 1/240 binary64)))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
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(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
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(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
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(* -1 (pow x 4))
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(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
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(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
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(* -1 (pow x 4))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
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(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
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(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))
(* -1 (pow x 2))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(* (pow x 2) (- (* 1/2 (pow x 2)) 1))
(.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2)))) 1))
(.f64 x (.f64 x (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))) #s(literal -1 binary64))))
(* (pow x 2) (- (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))) 1))
(.f64 (.f64 x x) (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))))) #s(literal -1 binary64)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))
(* -1 (* (pow x 2) (cos x)))
(-.f64 #s(literal 0 binary64) (.f64 (.f64 x x) (cos.f64 x)))

eval663.0ms (3.4%)

Compiler: Compiled 60748 to 3521 computations (94.2% saved)

prune477.0ms (2.5%)

Pruning

21 alts after pruning (17 fresh and 4 done)

	Pruned	Kept	Total
New	2253	13	2266
Fresh	9	4	13
Picked	2	3	5
Done	0	1	1
Total	2264	21	2285

Accuracy

100.0%

Counts

2285 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	51.8%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	53.5%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	25.6%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) x) x)
▶	53.4%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
	53.4%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	53.3%	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
▶	2.0%	(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
	45.5%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	52.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	17.4%	(/.f64 (.f64 (.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))
	12.9%	(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))
▶	45.5%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
	52.3%	(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	52.2%	(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (cos.f64 x) (*.f64 x x)))
	52.1%	(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
	52.3%	(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
	49.7%	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
▶	49.2%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
▶	76.0%	(*.f64 (/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	76.0%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	50.3%	#s(literal 1/2 binary64)

Compiler

Compiled 520 to 308 computations (40.8% saved)

simplify393.0ms (2%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	256	(/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x))))
✓	cost-diff	384	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	cost-diff	0	(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	cost-diff	128	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) (*.f64 x x))
✓	cost-diff	512	(-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))))
✓	cost-diff	1152	(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal -1/24 binary64) (.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
✓	cost-diff	0	(sin.f64 x)
✓	cost-diff	128	(/.f64 x (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	128	(/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	128	(*.f64 (/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (tan.f64 (/.f64 x #s(literal 2 binary64))))

Rules

1942×	`-lowering-.f32`
1942×	`-lowering-.f64`
1790×	`fma-lowering-fma.f32`
1790×	`fma-lowering-fma.f64`
1604×	`sum4-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	214
1	101	199
2	333	185
3	1732	168
4	6383	168
0	8323	168

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(* (/ (sin x) (/ x (/ 1 x))) (tan (/ x 2)))
(/ (sin x) (/ x (/ 1 x)))
(sin x)
x
(/ x (/ 1 x))
(/ 1 x)
1
(tan (/ x 2))
(/ x 2)
2
(+ 1/2 (* -1/24 (* x x)))
1/2
(* -1/24 (* x x))
-1/24
(* x x)
x
(/ (- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1)))) (* (- 0 (* x x)) (* x x)))
(- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1))))
(- 0 (* x x))
0
(* x x)
x
(* x (* x (+ (* 1/2 (* x x)) -1)))
(* x (+ (* 1/2 (* x x)) -1))
(+ (* 1/2 (* x x)) -1)
(* 1/2 (* x x))
1/2
-1
(* (- 0 (* x x)) (* x x))
(/ (/ 1 (/ x (- 1 (cos x)))) x)
(/ 1 (/ x (- 1 (cos x))))
1
(/ x (- 1 (cos x)))
x
(- 1 (cos x))
(cos x)
(/ 1 (/ (* x (* x x)) (- x (* x (cos x)))))
1
(/ (* x (* x x)) (- x (* x (cos x))))
(* x (* x x))
x
(* x x)
(- x (* x (cos x)))
(* x (cos x))
(cos x)

Outputs
(* (/ (sin x) (/ x (/ 1 x))) (tan (/ x 2)))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/ (sin x) (/ x (/ 1 x)))
(/.f64 (sin.f64 x) (*.f64 x x))
(sin x)
(sin.f64 x)
x
(/ x (/ 1 x))
(*.f64 x x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
(tan (/ x 2))
(tan.f64 (/.f64 x #s(literal 2 binary64)))
(/ x 2)
(/.f64 x #s(literal 2 binary64))
2
#s(literal 2 binary64)
(+ 1/2 (* -1/24 (* x x)))
(+.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x #s(literal -1/24 binary64))))
1/2
#s(literal 1/2 binary64)
(* -1/24 (* x x))
(.f64 x (.f64 x #s(literal -1/24 binary64)))
-1/24
#s(literal -1/24 binary64)
(* x x)
(*.f64 x x)
x
(/ (- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1)))) (* (- 0 (* x x)) (* x x)))
(/.f64 (/.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) x) x)
(- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1))))
(.f64 x (.f64 x (.f64 (.f64 x x) #s(literal -1/2 binary64))))
(- 0 (* x x))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
0
#s(literal 0 binary64)
(* x x)
(*.f64 x x)
x
(* x (* x (+ (* 1/2 (* x x)) -1)))
(.f64 x (.f64 x (+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))))
(* x (+ (* 1/2 (* x x)) -1))
(.f64 x (+.f64 (.f64 x (*.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(+ (* 1/2 (* x x)) -1)
(+.f64 (.f64 x (.f64 x #s(literal 1/2 binary64))) #s(literal -1 binary64))
(* 1/2 (* x x))
(.f64 x (.f64 x #s(literal 1/2 binary64)))
1/2
#s(literal 1/2 binary64)
-1
#s(literal -1 binary64)
(* (- 0 (* x x)) (* x x))
(-.f64 #s(literal 0 binary64) (.f64 x (.f64 x (*.f64 x x))))
(/ (/ 1 (/ x (- 1 (cos x)))) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/ 1 (/ x (- 1 (cos x))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
1
#s(literal 1 binary64)
(/ x (- 1 (cos x)))
(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
x
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)
(/ 1 (/ (* x (* x x)) (- x (* x (cos x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
1
#s(literal 1 binary64)
(/ (* x (* x x)) (- x (* x (cos x))))
(/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(- x (* x (cos x)))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (cos x))
(*.f64 x (cos.f64 x))
(cos x)
(cos.f64 x)

localize717.0ms (3.7%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(*.f64 x (cos.f64 x))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
✓	accuracy	84.9%	(-.f64 x (*.f64 x (cos.f64 x)))
✓	accuracy	62.0%	(/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x))))
✓	accuracy	99.9%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
✓	accuracy	99.3%	(/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	accuracy	77.4%	(/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	accuracy	77.3%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	99.9%	(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
✓	accuracy	99.8%	(.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x))
✓	accuracy	89.6%	(-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))))
✓	accuracy	30.2%	(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
✓	accuracy	99.4%	(.f64 #s(literal -1/24 binary64) (.f64 x x))
✓	accuracy	100.0%	(tan.f64 (/.f64 x #s(literal 2 binary64)))
✓	accuracy	99.8%	(/.f64 x (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(*.f64 (/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	accuracy	77.1%	(/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x)))

Results

187.0ms	60×	2	valid
153.0ms	133×	0	valid
129.0ms	25×	3	valid
75.0ms	38×	1	valid

Compiler

Compiled 238 to 36 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 330.0ms

ival-mult: 76.0ms (23% of total)

ival-div: 71.0ms (21.5% of total)

ival-cos: 50.0ms (15.1% of total)

backward-pass: 40.0ms (12.1% of total)

ival-sin: 30.0ms (9.1% of total)

ival-sub: 24.0ms (7.3% of total)

ival-tan: 13.0ms (3.9% of total)

ival-add: 12.0ms (3.6% of total)

...c/correct-round.rkt:119:19: 11.0ms (3.3% of total)

const: 3.0ms (0.9% of total)

series27.0ms (0.1%)

Counts

22 → 264

Calls

Call 1

Inputs
#<alt (* (/ (sin x) (/ x (/ 1 x))) (tan (/ x 2)))>
#<alt (/ (sin x) (/ x (/ 1 x)))>
#<alt (/ x (/ 1 x))>
#<alt (sin x)>
#<alt (+ 1/2 (* -1/24 (* x x)))>
#<alt (* -1/24 (* x x))>
#<alt (* x x)>
#<alt (/ (- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1)))) (* (- 0 (* x x)) (* x x)))>
#<alt (- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1))))>
#<alt (- 0 (* x x))>
#<alt (/ (/ 1 (/ x (- 1 (cos x)))) x)>
#<alt (/ 1 (/ x (- 1 (cos x))))>
#<alt (/ x (- 1 (cos x)))>
#<alt (- 1 (cos x))>
#<alt (/ 1 (/ (* x (* x x)) (- x (* x (cos x)))))>
#<alt (/ (* x (* x x)) (- x (* x (cos x))))>
#<alt (* x (* x x))>
#<alt (tan (/ x 2))>
#<alt (* (- 0 (* x x)) (* x x))>
#<alt (* x (+ (* 1/2 (* x x)) -1))>
#<alt (- x (* x (cos x)))>
#<alt (* x (cos x))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/6 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (/ (sin x) (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt x>
#<alt (* x (+ 1 (* -1/6 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt (sin x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (* -1/24 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1/2 (pow x 4))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt (* -1 (pow x 2))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ 2 x)>
#<alt (/ (+ 2 (* 1/6 (pow x 2))) x)>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) x)>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (/ x (- 1 (cos x)))>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (/ (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (/ (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (/ (pow x 2) (+ 1 (* -1 (cos x))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))>
#<alt (* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (/ (sin (* 1/2 x)) (cos (* 1/2 x)))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 (pow x 4))>
#<alt (* -1 x)>
#<alt (* x (- (* 1/2 (pow x 2)) 1))>
#<alt (* x (- (* 1/2 (pow x 2)) 1))>
#<alt (* x (- (* 1/2 (pow x 2)) 1))>
#<alt (* 1/2 (pow x 3))>
#<alt (* (pow x 3) (- 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/2 (/ 1 (pow x 2))))>
#<alt (* (pow x 3) (- 1/2 (/ 1 (pow x 2))))>
#<alt (* 1/2 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))>
#<alt (* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))>
#<alt (* 1/2 (pow x 3))>
#<alt (* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (- 1 (cos x)))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt (* x (+ 1 (* -1 (cos x))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (pow x 2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))>
#<alt (* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>
#<alt (* x (cos x))>

Calls

66 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(/ (- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1)))) (* (- 0 (* x x)) (* x x)))
2.0ms	x	@	inf	(/ 1 (/ (* x (* x x)) (- x (* x (cos x)))))
1.0ms	x	@	-inf	(/ (* x (* x x)) (- x (* x (cos x))))
1.0ms	x	@	-inf	(/ x (- 1 (cos x)))
1.0ms	x	@	inf	(/ x (- 1 (cos x)))

rewrite828.0ms (4.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2602×	`-lowering-.f32`
2602×	`-lowering-.f64`
2346×	`/-lowering-/.f32`
2346×	`/-lowering-/.f64`
1542×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	162
1	239	141
2	2092	131
0	9194	131

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 1058

Calls

Call 1

Inputs
(* (/ (sin x) (/ x (/ 1 x))) (tan (/ x 2)))
(/ (sin x) (/ x (/ 1 x)))
(/ x (/ 1 x))
(sin x)
(+ 1/2 (* -1/24 (* x x)))
(* -1/24 (* x x))
(* x x)
(/ (- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1)))) (* (- 0 (* x x)) (* x x)))
(- (- 0 (* x x)) (* x (* x (+ (* 1/2 (* x x)) -1))))
(- 0 (* x x))
(/ (/ 1 (/ x (- 1 (cos x)))) x)
(/ 1 (/ x (- 1 (cos x))))
(/ x (- 1 (cos x)))
(- 1 (cos x))
(/ 1 (/ (* x (* x x)) (- x (* x (cos x)))))
(/ (* x (* x x)) (- x (* x (cos x))))
(* x (* x x))
(tan (/ x 2))
(* (- 0 (* x x)) (* x x))
(* x (+ (* 1/2 (* x x)) -1))
(- x (* x (cos x)))
(* x (cos x))

Outputs
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))))
(/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (/.f64 (*.f64 x x) (sin.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x)) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x)))
(/.f64 (neg.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 x x))
(/.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64)))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64)) (/.f64 (.f64 x x) (sin.f64 x)))
(/.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x))) (.f64 x x))
(/.f64 (.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 (.f64 x x) (sin.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (.f64 x x))
(/.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x))) (cos.f64 (/.f64 x #s(literal 2 binary64))))
(/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x) x)
(/.f64 (neg.f64 (.f64 (sin.f64 x) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (tan.f64 (/.f64 x #s(literal 2 binary64)))) (neg.f64 (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (.f64 (/.f64 (*.f64 x x) (sin.f64 x)) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (.f64 (*.f64 x x) (cos.f64 (/.f64 x #s(literal 2 binary64))))))
(/.f64 (neg.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (sin.f64 x))) (neg.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(/.f64 (neg.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (*.f64 x x) (sin.f64 x)))))
(/.f64 (neg.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (neg.f64 (.f64 (cos.f64 (/.f64 x #s(literal 2 binary64))) (*.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))) (.f64 x x))
(/.f64 (neg.f64 (.f64 (/.f64 (sin.f64 x) (.f64 x x)) (sin.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) #s(literal 1 binary64))) (neg.f64 (/.f64 (.f64 x x) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (.f64 x x))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (neg.f64 (/.f64 (.f64 x x) (sin.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))) (.f64 x x))
(/.f64 (neg.f64 (.f64 (sin.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))) (neg.f64 (cos.f64 (/.f64 x #s(literal 2 binary64)))))
(/.f64 (neg.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64))))) #s(literal -1 binary64))
(.f64 (sin.f64 x) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(.f64 (sin.f64 x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (.f64 x x)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) (.f64 x x)))
(.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) x))
(.f64 (/.f64 (sin.f64 x) x) (.f64 (/.f64 #s(literal 1 binary64) x) (tan.f64 (/.f64 x #s(literal 2 binary64)))))
(.f64 (.f64 (tan.f64 (/.f64 x #s(literal 2 binary64))) (/.f64 (sin.f64 x) x)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 (.f64 (sin.f64 x) (tan.f64 (/.f64 x #s(literal 2 binary64)))) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (sin.f64 x))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (sin.f64 x) (*.f64 x x)))
(/.f64 (sin.f64 x) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (sin.f64 x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (*.f64 x x) (sin.f64 x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) (sin.f64 x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (sin.f64 x) x) x)
(/.f64 (.f64 (sin.f64 x) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (.f64 (sin.f64 x) #s(literal -1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x))) (*.f64 x x))
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) #s(literal 1 binary64)) x)
(/.f64 (*.f64 (/.f64 (sin.f64 x) x) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (/.f64 (sin.f64 x) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (.f64 (sin.f64 x) #s(literal 1 binary64))) (.f64 x x))
(/.f64 (neg.f64 (.f64 (sin.f64 x) #s(literal -1 binary64))) (.f64 x x))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)))) (*.f64 x x))
(/.f64 (neg.f64 (*.f64 (/.f64 (sin.f64 x) x) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (*.f64 (/.f64 (sin.f64 x) x) #s(literal -1 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(pow.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) (sin.f64 x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 (sin.f64 x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 (sin.f64 x) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (sin.f64 x) x))
(.f64 (-.f64 #s(literal 0 binary64) (sin.f64 x)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (sin.f64 x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (sin.f64 x)) #s(literal -1 binary64)))
(*.f64 (/.f64 (sin.f64 x) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (.f64 (/.f64 (sin.f64 x) x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (sin.f64 x) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 (sin.f64 x) (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x))
(+.f64 (*.f64 x x) #s(literal 0 binary64))
(+.f64 #s(literal 0 binary64) (*.f64 x x))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (*.f64 x x))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x))
(-.f64 (/.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x))
(fma.f64 x x #s(literal 0 binary64))
(fma.f64 x (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 x x) #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) x #s(literal 0 binary64))
(fma.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)) #s(literal 0 binary64))
(fma.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal 0 binary64))
(fma.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 0 binary64))
(fma.f64 (/.f64 x #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x) #s(literal 0 binary64))
(neg.f64 (*.f64 x x))
(/.f64 x (/.f64 #s(literal 1 binary64) x))
(/.f64 x (/.f64 #s(literal -1 binary64) x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)))
(/.f64 (*.f64 x x) #s(literal 1 binary64))
(/.f64 (*.f64 x x) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) x))
(/.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal -1 binary64) x))
(/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 x x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) (/.f64 #s(literal -1 binary64) x))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))) (/.f64 #s(literal -1 binary64) x))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 x (-.f64 #s(literal 0 binary64) x))
(.f64 #s(literal 1 binary64) (.f64 x x))
(.f64 (.f64 x x) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (.f64 x x))
(*.f64 (-.f64 #s(literal 0 binary64) x) x)
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(*.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal -1 binary64) x)))
(.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (*.f64 x x)))))
(.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 x (.f64 x (*.f64 x x))))
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(/.f64 (neg.f64 (-.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x))) (.f64 #s(literal 1/2 binary64) (.f64 x (.f64 x x)))) (.f64 x x))) (neg.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))))) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 x (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)))) (neg.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal -1 binary64) (.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 x (.f64 x x)) #s(literal 8 binary64)))) x)) (neg.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (.f64 x (.f64 x (.f64 x x)))) #s(literal -1 binary64)) x)) (neg.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal 1 binary64))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)))
(.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (*.f64 x x)) #s(literal -1 binary64)) x)
(+.f64 x (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(+.f64 (-.f64 x (.f64 x (cos.f64 x))) (fma.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) x (.f64 x (cos.f64 x))))
(+.f64 (-.f64 x (.f64 x (cos.f64 x))) (fma.f64 (-.f64 #s(literal 0 binary64) x) (cos.f64 x) (.f64 x (cos.f64 x))))
(+.f64 (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)) x)
(-.f64 x (*.f64 x (cos.f64 x)))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))) (/.f64 (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64)) (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))))
(-.f64 (/.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)) (/.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(fma.f64 x #s(literal 1 binary64) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 x (-.f64 #s(literal 0 binary64) (cos.f64 x)) x)
(fma.f64 #s(literal 1 binary64) x (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 #s(literal -1 binary64) (*.f64 x (cos.f64 x)) x)
(fma.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x) (*.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))
(fma.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x) x)
(fma.f64 (-.f64 #s(literal 0 binary64) x) (cos.f64 x) x)
(fma.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) x x)
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (*.f64 x (cos.f64 x)) #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (*.f64 x (cos.f64 x)) #s(literal 3 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 x (.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (-.f64 x (.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64)))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (.f64 x (.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (neg.f64 (-.f64 x (.f64 (cos.f64 x) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))) (.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64)))) (.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) (.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))))) (neg.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))))
(pow.f64 (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (*.f64 x (cos.f64 x)) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x) (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (.f64 x (cos.f64 x)) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 x (cos.f64 x)) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))))
(.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (/.f64 #s(literal 1 binary64) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(*.f64 x (cos.f64 x))
(*.f64 (cos.f64 x) x)

simplify619.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

3146×	`-lowering-.f32`
3146×	`-lowering-.f64`
2724×	`+-lowering-+.f64`
2724×	`+-lowering-+.f32`
1454×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	146	1695
1	428	1626
2	1210	1603
3	3670	1594
4	5156	1594
5	7979	1594
0	8159	1594

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ (* (sin x) (sin (* 1/2 x))) (* (pow x 2) (cos (* 1/2 x))))
(/ 1 x)
(/ (+ 1 (* -1/6 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))) x)
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(/ (sin x) (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
x
(* x (+ 1 (* -1/6 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/120 (pow x 2)) 1/6))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/120 (* -1/5040 (pow x 2)))) 1/6))))
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
(sin x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* -1/24 (pow x 2)))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* (pow x 2) (- (* 1/2 (/ 1 (pow x 2))) 1/24))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(* -1/24 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1/2 (pow x 4))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
(* -1 (pow x 2))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ 2 x)
(/ (+ 2 (* 1/6 (pow x 2))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) x)
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) x)
(/ x (- 1 (cos x)))
(/ x (- 1 (cos x)))
(/ x (- 1 (cos x)))
(/ x (- 1 (cos x)))
(/ x (- 1 (cos x)))
(/ x (- 1 (cos x)))
(/ x (- 1 (cos x)))
(/ x (- 1 (cos x)))
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (+ 1 (* -1 (cos x))))
(/ (pow x 2) (+ 1 (* -1 (cos x))))
(/ (pow x 2) (+ 1 (* -1 (cos x))))
(/ (pow x 2) (+ 1 (* -1 (cos x))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/2 x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 (pow x 4))
(* -1 x)
(* x (- (* 1/2 (pow x 2)) 1))
(* x (- (* 1/2 (pow x 2)) 1))
(* x (- (* 1/2 (pow x 2)) 1))
(* 1/2 (pow x 3))
(* (pow x 3) (- 1/2 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/2 (/ 1 (pow x 2))))
(* (pow x 3) (- 1/2 (/ 1 (pow x 2))))
(* 1/2 (pow x 3))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))
(* 1/2 (pow x 3))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (- 1 (cos x)))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
(* x (+ 1 (* -1 (cos x))))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))
(* x (cos x))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
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(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* 1/24 (pow x 2))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64)))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* 1/240 (pow x 2))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/240 binary64))))))
(* x (+ 1/2 (* (pow x 2) (+ 1/24 (* (pow x 2) (+ 1/240 (* 17/40320 (pow x 2))))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/24 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/240 binary64) (.f64 (*.f64 x x) #s(literal 17/40320 binary64)))))))))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(/ (sin (* 1/2 x)) (cos (* 1/2 x)))
(/.f64 (sin.f64 (.f64 #s(literal 1/2 binary64) x)) (cos.f64 (.f64 #s(literal 1/2 binary64) x)))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 (pow x 4))
(.f64 x (.f64 x (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (* 1/2 (pow x 2)) 1))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* x (- (* 1/2 (pow x 2)) 1))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* x (- (* 1/2 (pow x 2)) 1))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* 1/2 (pow x 3))
(.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(* (pow x 3) (- 1/2 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* (pow x 3) (- 1/2 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* (pow x 3) (- 1/2 (/ 1 (pow x 2))))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* 1/2 (pow x 3))
(.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* -1 (* (pow x 3) (- (/ 1 (pow x 2)) 1/2)))
(.f64 x (+.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* 1/2 (pow x 3))
(.f64 x (.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(* (pow x 3) (+ 1/2 (* -1/24 (pow x 2))))
(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (*.f64 x x)))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))))))
(* (pow x 3) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(.f64 x (.f64 x (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (*.f64 x x) #s(literal -1/40320 binary64))))))))))
(* x (- 1 (cos x)))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (- 1 (cos x)))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (- 1 (cos x)))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (- 1 (cos x)))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (+ 1 (* -1 (cos x))))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (+ 1 (* -1 (cos x))))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (+ 1 (* -1 (cos x))))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x (+ 1 (* -1 (cos x))))
(*.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))
x
(* x (+ 1 (* -1/2 (pow x 2))))
(.f64 x (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (*.f64 x x))))
(* x (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (*.f64 x #s(literal 1/24 binary64))))))))
(* x (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/2 binary64) (.f64 (.f64 x x) (-.f64 #s(literal 1/24 binary64) (.f64 (*.f64 x x) #s(literal 1/720 binary64))))))))
(* x (cos x))
(*.f64 x (cos.f64 x))
(* x (cos x))
(*.f64 x (cos.f64 x))
(* x (cos x))
(*.f64 x (cos.f64 x))
(* x (cos x))
(*.f64 x (cos.f64 x))
(* x (cos x))
(*.f64 x (cos.f64 x))
(* x (cos x))
(*.f64 x (cos.f64 x))
(* x (cos x))
(*.f64 x (cos.f64 x))
(* x (cos x))
(*.f64 x (cos.f64 x))

eval504.0ms (2.6%)

Compiler: Compiled 46902 to 4029 computations (91.4% saved)

prune604.0ms (3.1%)

Pruning

25 alts after pruning (19 fresh and 6 done)

	Pruned	Kept	Total
New	1714	10	1724
Fresh	3	9	12
Picked	3	2	5
Done	0	4	4
Total	1720	25	1745

Accuracy

100.0%

Counts

1745 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.4%	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
	52.2%	(/.f64 (/.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x))
	51.8%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	53.5%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	25.6%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) x) x)
	75.4%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) x)) x)
▶	50.1%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)
	53.4%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
▶	53.3%	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
	45.5%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	52.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	17.4%	(/.f64 (.f64 (.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))
	53.0%	(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
▶	73.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))))
	72.8%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x #s(literal 1/3024 binary64)))))))))
▶	75.6%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
	53.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
▶	52.3%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
	52.2%	(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (cos.f64 x) (*.f64 x x)))
	52.1%	(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
	49.7%	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
✓	49.2%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
✓	76.0%	(*.f64 (/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	76.0%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	50.3%	#s(literal 1/2 binary64)

Compiler

Compiled 556 to 360 computations (35.3% saved)

simplify404.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	128	(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	cost-diff	256	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	cost-diff	0	(/.f64 (cos.f64 x) x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	128	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x))
✓	cost-diff	128	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64))))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))))
✓	cost-diff	0	(/.f64 #s(literal 2 binary64) x)
✓	cost-diff	128	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	cost-diff	384	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 (.f64 x x) #s(literal 1/6 binary64))
✓	cost-diff	0	(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))

Rules

2196×	`fnmadd-define`
1780×	`sum3-define`
1732×	`fma-define`
1712×	`sum5-define`
1114×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	158
1	72	153
2	157	149
3	324	146
4	557	146
5	865	146
6	1778	146
7	2820	146
8	3920	146
9	6501	146
0	8052	146

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ 2 (* (* x x) 1/6)))
1
(+ 2 (* (* x x) 1/6))
2
(* (* x x) 1/6)
(* x x)
x
1/6
(/ (/ 1 (/ 2 x)) x)
(/ 1 (/ 2 x))
1
(/ 2 x)
2
x
(/ 1 (+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6))))
1
(+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6)))
2
(* (* x x) (+ (* x (* x 1/120)) 1/6))
(* x x)
x
(+ (* x (* x 1/120)) 1/6)
(* x (* x 1/120))
(* x 1/120)
1/120
1/6
(/ (- (/ 1 x) (/ (cos x) x)) x)
(- (/ 1 x) (/ (cos x) x))
(/ 1 x)
1
x
(/ (cos x) x)
(cos x)
(/ 1 (* (* x x) (/ 1 (- 1 (cos x)))))
1
(* (* x x) (/ 1 (- 1 (cos x))))
(* x x)
x
(/ 1 (- 1 (cos x)))
(- 1 (cos x))
(cos x)

Outputs
(/ 1 (+ 2 (* (* x x) 1/6)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
1
#s(literal 1 binary64)
(+ 2 (* (* x x) 1/6))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
2
#s(literal 2 binary64)
(* (* x x) 1/6)
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* x x)
(*.f64 x x)
x
1/6
#s(literal 1/6 binary64)
(/ (/ 1 (/ 2 x)) x)
#s(literal 1/2 binary64)
(/ 1 (/ 2 x))
(*.f64 x #s(literal 1/2 binary64))
1
#s(literal 1 binary64)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
2
#s(literal 2 binary64)
x
(/ 1 (+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))))
1
#s(literal 1 binary64)
(+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6)))
(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))))
2
#s(literal 2 binary64)
(* (* x x) (+ (* x (* x 1/120)) 1/6))
(.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64)))))
(* x x)
(*.f64 x x)
x
(+ (* x (* x 1/120)) 1/6)
(+.f64 #s(literal 1/6 binary64) (.f64 x (.f64 x #s(literal 1/120 binary64))))
(* x (* x 1/120))
(.f64 x (.f64 x #s(literal 1/120 binary64)))
(* x 1/120)
(*.f64 x #s(literal 1/120 binary64))
1/120
#s(literal 1/120 binary64)
1/6
#s(literal 1/6 binary64)
(/ (- (/ 1 x) (/ (cos x) x)) x)
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(- (/ 1 x) (/ (cos x) x))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(/ (cos x) x)
(/.f64 (cos.f64 x) x)
(cos x)
(cos.f64 x)
(/ 1 (* (* x x) (/ 1 (- 1 (cos x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
1
#s(literal 1 binary64)
(* (* x x) (/ 1 (- 1 (cos x))))
(/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(* x x)
(*.f64 x x)
x
(/ 1 (- 1 (cos x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(cos x)
(cos.f64 x)

localize641.0ms (3.3%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	accuracy	77.3%	(-.f64 #s(literal 1 binary64) (cos.f64 x))
✓	accuracy	75.9%	(.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	accuracy	100.0%	(cos.f64 x)
✓	accuracy	99.9%	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
✓	accuracy	99.8%	(/.f64 (cos.f64 x) x)
✓	accuracy	54.1%	(-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x))
✓	accuracy	99.8%	(*.f64 x #s(literal 1/120 binary64))
✓	accuracy	99.8%	(.f64 x (.f64 x #s(literal 1/120 binary64)))
✓	accuracy	99.8%	(.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))))
✓	accuracy	100.0%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)
✓	accuracy	100.0%	(/.f64 #s(literal 2 binary64) x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x))
✓	accuracy	100.0%	(+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
✓	accuracy	99.4%	(.f64 (.f64 x x) #s(literal 1/6 binary64))

Results

196.0ms	60×	2	valid
146.0ms	133×	0	valid
98.0ms	25×	3	valid
66.0ms	38×	1	valid

Compiler

Compiled 178 to 28 computations (84.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 279.0ms

ival-div: 78.0ms (27.9% of total)

ival-mult: 68.0ms (24.4% of total)

ival-cos: 50.0ms (17.9% of total)

backward-pass: 36.0ms (12.9% of total)

...c/correct-round.rkt:119:19: 20.0ms (7.2% of total)

ival-add: 15.0ms (5.4% of total)

ival-sub: 12.0ms (4.3% of total)

const: 1.0ms (0.4% of total)

series40.0ms (0.2%)

Counts

21 → 252

Calls

Call 1

Inputs
#<alt (/ 1 (+ 2 (* (* x x) 1/6)))>
#<alt (+ 2 (* (* x x) 1/6))>
#<alt (* (* x x) 1/6)>
#<alt (* x x)>
#<alt (/ (/ 1 (/ 2 x)) x)>
#<alt (/ 1 (/ 2 x))>
#<alt (/ 2 x)>
#<alt (/ 1 (+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6))))>
#<alt (+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6)))>
#<alt (* (* x x) (+ (* x (* x 1/120)) 1/6))>
#<alt (/ (- (/ 1 x) (/ (cos x) x)) x)>
#<alt (- (/ 1 x) (/ (cos x) x))>
#<alt (/ 1 x)>
#<alt (/ (cos x) x)>
#<alt (/ 1 (* (* x x) (/ 1 (- 1 (cos x)))))>
#<alt (* (* x x) (/ 1 (- 1 (cos x))))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (* x (* x 1/120))>
#<alt (* x 1/120)>
#<alt (cos x)>
#<alt (- 1 (cos x))>

Outputs
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))>
#<alt (/ 6 (pow x 2))>
#<alt (/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))>
#<alt (/ 6 (pow x 2))>
#<alt (/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))>
#<alt (/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (* 1/6 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt 1/2>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt (/ 2 x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* 1/17280 (pow x 2)))) 1/24)))>
#<alt (/ 120 (pow x 4))>
#<alt (/ (- 120 (* 2400 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 120 (/ 19200 (pow x 4))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 120 (+ (* 192000 (/ 1 (pow x 6))) (/ 19200 (pow x 4)))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ 120 (pow x 4))>
#<alt (/ (- 120 (* 2400 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 120 (/ 19200 (pow x 4))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))>
#<alt (/ (- (+ 120 (+ (* 192000 (/ 1 (pow x 6))) (/ 19200 (pow x 4)))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))>
#<alt 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))>
#<alt (* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))>
#<alt (* 1/6 (pow x 2))>
#<alt (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* 1/120 (pow x 4))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt (* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (/ (+ 1 (* -1 (cos x))) (pow x 2))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (- 1 (cos x)) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ (+ 1 (* -1 (cos x))) x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ (+ 1 (* -1/2 (pow x 2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)>
#<alt (/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt (/ (cos x) x)>
#<alt 1/2>
#<alt (+ 1/2 (* -1/24 (pow x 2)))>
#<alt (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))>
#<alt (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt (/ (- 1 (cos x)) (pow x 2))>
#<alt 2>
#<alt (+ 2 (* 1/6 (pow x 2)))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))>
#<alt (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ (pow x 2) (- 1 (cos x)))>
#<alt (/ 2 (pow x 2))>
#<alt (/ (+ 2 (* 1/6 (pow x 2))) (pow x 2))>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) (pow x 2))>
#<alt (/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) (pow x 2))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (/ 1 (- 1 (cos x)))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 (pow x 2))>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt (* 1/120 x)>
#<alt 1>
#<alt (+ 1 (* -1/2 (pow x 2)))>
#<alt (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))>
#<alt (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (cos x)>
#<alt (* 1/2 (pow x 2))>
#<alt (* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))>
#<alt (* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>
#<alt (- 1 (cos x))>

Calls

63 calls:

Time	Variable		Point	Expression
7.0ms	x	@	-inf	(+ 2 (* (* x x) 1/6))
4.0ms	x	@	-inf	(/ (- (/ 1 x) (/ (cos x) x)) x)
4.0ms	x	@	inf	(* x (* x 1/120))
2.0ms	x	@	inf	(/ (- (/ 1 x) (/ (cos x) x)) x)
1.0ms	x	@	-inf	(* (* x x) (/ 1 (- 1 (cos x))))

rewrite922.0ms (4.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4140×	`/-lowering-/.f32`
4140×	`/-lowering-/.f64`
3190×	`-lowering-.f32`
3190×	`-lowering-.f64`
2322×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	124
1	200	120
2	1684	120
0	8437	120

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 984

Calls

Call 1

Inputs
(/ 1 (+ 2 (* (* x x) 1/6)))
(+ 2 (* (* x x) 1/6))
(* (* x x) 1/6)
(* x x)
(/ (/ 1 (/ 2 x)) x)
(/ 1 (/ 2 x))
(/ 2 x)
(/ 1 (+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6))))
(+ 2 (* (* x x) (+ (* x (* x 1/120)) 1/6)))
(* (* x x) (+ (* x (* x 1/120)) 1/6))
(/ (- (/ 1 x) (/ (cos x) x)) x)
(- (/ 1 x) (/ (cos x) x))
(/ 1 x)
(/ (cos x) x)
(/ 1 (* (* x x) (/ 1 (- 1 (cos x)))))
(* (* x x) (/ 1 (- 1 (cos x))))
(/ 1 (- 1 (cos x)))
(* x (* x 1/120))
(* x 1/120)
(cos x)
(- 1 (cos x))

Outputs
(exp.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 #s(literal -2 binary64) (neg.f64 (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal -1 binary64) (+.f64 #s(literal -2 binary64) (neg.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (+.f64 #s(literal -2 binary64) (neg.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))))))))
(pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) #s(literal -1 binary64))
(pow.f64 (neg.f64 (+.f64 #s(literal -2 binary64) (neg.f64 (.f64 x (.f64 x #s(literal 1/6 binary64)))))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal 1 binary64))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))))
(.f64 (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x)))) #s(literal -1 binary64)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))
(exp.f64 (neg.f64 (.f64 (log.f64 (+.f64 #s(literal 2 binary64) (.f64 x (*.f64 x #s(literal 1/6 binary64))))) #s(literal -1 binary64))))
(-.f64 (/.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (/.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(fma.f64 x (*.f64 x #s(literal 1/6 binary64)) #s(literal 2 binary64))
(fma.f64 (*.f64 x x) #s(literal 1/6 binary64) #s(literal 2 binary64))
(fma.f64 #s(literal 1/6 binary64) (*.f64 x x) #s(literal 2 binary64))
(fma.f64 (*.f64 x #s(literal 1/6 binary64)) x #s(literal 2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))))
(/.f64 (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (*.f64 x x))))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x)))))))
(/.f64 (+.f64 #s(literal -2 binary64) (neg.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))))) #s(literal -1 binary64))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))
(/.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/3 binary64) (.f64 x x)))))
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(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (neg.f64 (+.f64 #s(literal 1 binary64) (-.f64 (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (neg.f64 (*.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) (neg.f64 (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (cos.f64 x)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) #s(literal 1 binary64))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))) (.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (*.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x)))))) (neg.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (*.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x)))) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (cos.f64 x)) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (.f64 #s(literal 2 binary64) x))))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))
(*.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))) #s(literal -1 binary64)))
(.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))
(*.f64 (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) #s(literal -1/2 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (cos.f64 x) #s(literal 3 binary64)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (cos.f64 x) (+.f64 #s(literal 1 binary64) (cos.f64 x))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/2 binary64) (cos.f64 (*.f64 #s(literal 2 binary64) x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (cos.f64 x))))

simplify544.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2274×	`-lowering-.f32`
2274×	`-lowering-.f64`
1768×	`sum3-define`
1734×	`+-lowering-+.f64`
1734×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	1621
1	396	1547
2	1059	1543
3	2805	1531
4	5463	1531
0	8184	1531

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

Inputs
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/ 6 (pow x 2))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* 1/6 (pow x 2)))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(* 1/6 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
1/2
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
(/ 2 x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* 1/17280 (pow x 2)))) 1/24)))
(/ 120 (pow x 4))
(/ (- 120 (* 2400 (/ 1 (pow x 2)))) (pow x 4))
(/ (- (+ 120 (/ 19200 (pow x 4))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))
(/ (- (+ 120 (+ (* 192000 (/ 1 (pow x 6))) (/ 19200 (pow x 4)))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))
(/ 120 (pow x 4))
(/ (- 120 (* 2400 (/ 1 (pow x 2)))) (pow x 4))
(/ (- (+ 120 (/ 19200 (pow x 4))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))
(/ (- (+ 120 (+ (* 192000 (/ 1 (pow x 6))) (/ 19200 (pow x 4)))) (* 2400 (/ 1 (pow x 2)))) (pow x 4))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))
(* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))
(* 1/120 (pow x 4))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))
(* (pow x 4) (+ 1/120 (+ (* 1/6 (/ 1 (pow x 2))) (/ 2 (pow x 4)))))
(* 1/6 (pow x 2))
(* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))
(* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))
(* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))
(* 1/120 (pow x 4))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* 1/120 (pow x 4))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
(* (pow x 4) (+ 1/120 (* 1/6 (/ 1 (pow x 2)))))
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(/ (+ 1 (* -1 (cos x))) (pow x 2))
(* 1/2 x)
(* x (+ 1/2 (* -1/24 (pow x 2))))
(* x (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* x (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (- 1 (cos x)) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ (+ 1 (* -1 (cos x))) x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ (+ 1 (* -1/2 (pow x 2))) x)
(/ (+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2))) x)
(/ (+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2))) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
(/ (cos x) x)
1/2
(+ 1/2 (* -1/24 (pow x 2)))
(+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24)))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24)))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
(/ (- 1 (cos x)) (pow x 2))
2
(+ 2 (* 1/6 (pow x 2)))
(+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2)))))
(+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2)))))))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ (pow x 2) (- 1 (cos x)))
(/ 2 (pow x 2))
(/ (+ 2 (* 1/6 (pow x 2))) (pow x 2))
(/ (+ 2 (* (pow x 2) (+ 1/6 (* 1/120 (pow x 2))))) (pow x 2))
(/ (+ 2 (* (pow x 2) (+ 1/6 (* (pow x 2) (+ 1/120 (* 1/3024 (pow x 2))))))) (pow x 2))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(/ 1 (- 1 (cos x)))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 (pow x 2))
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
(* 1/120 x)
1
(+ 1 (* -1/2 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/24 (pow x 2)) 1/2)))
(+ 1 (* (pow x 2) (- (* (pow x 2) (+ 1/24 (* -1/720 (pow x 2)))) 1/2)))
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(cos x)
(* 1/2 (pow x 2))
(* (pow x 2) (+ 1/2 (* -1/24 (pow x 2))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* 1/720 (pow x 2)) 1/24))))
(* (pow x 2) (+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/720 (* -1/40320 (pow x 2)))) 1/24))))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))
(- 1 (cos x))

Outputs
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/24 (pow x 2)))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(+ 1/2 (* (pow x 2) (- (* 1/288 (pow x 2)) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/288 binary64)))))
(+ 1/2 (* (pow x 2) (- (* (pow x 2) (+ 1/288 (* -1/3456 (pow x 2)))) 1/24)))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/288 binary64) (.f64 (.f64 x x) #s(literal -1/3456 binary64)))))))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -72 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (+.f64 (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -72 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (+.f64 (+.f64 (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -72 binary64) (.f64 x x))) (/.f64 #s(literal -10368 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x x))
(/ 6 (pow x 2))
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(/ (- 6 (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (/.f64 #s(literal -72 binary64) (.f64 x x))) (.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (* 72 (/ 1 (pow x 2)))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (+.f64 (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -72 binary64) (.f64 x x)))) (*.f64 x x))
(/ (- (+ 6 (/ 864 (pow x 4))) (+ (* 72 (/ 1 (pow x 2))) (* 10368 (/ 1 (pow x 6))))) (pow x 2))
(/.f64 (+.f64 #s(literal 6 binary64) (+.f64 (+.f64 (/.f64 #s(literal 864 binary64) (.f64 x (.f64 x (.f64 x x)))) (/.f64 #s(literal -72 binary64) (.f64 x x))) (/.f64 #s(literal -10368 binary64) (.f64 x (.f64 x (.f64 x (.f64 x (.f64 x x)))))))) (.f64 x x))
2
#s(literal 2 binary64)
(+ 2 (* 1/6 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+ 2 (* 1/6 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(+ 2 (* 1/6 (pow x 2)))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* (pow x 2) (+ 1/6 (* 2 (/ 1 (pow x 2)))))
(+.f64 #s(literal 2 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 x #s(literal 1/6 binary64)))
(* 1/6 (pow x 2))
(.f64 x (.f64 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)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
1/2
#s(literal 1/2 binary64)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
(/.f64 #s(literal 2 binary64) x)
(/ 2 x)
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#s(literal 2 binary64)
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(.f64 (.f64 x x) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/720 binary64) (.f64 (.f64 x x) #s(literal -1/40320 binary64))))))))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))
(- 1 (cos x))
(-.f64 #s(literal 1 binary64) (cos.f64 x))

eval412.0ms (2.1%)

Compiler: Compiled 24861 to 2588 computations (89.6% saved)

prune306.0ms (1.6%)

Pruning

34 alts after pruning (26 fresh and 8 done)

	Pruned	Kept	Total
New	1276	15	1291
Fresh	3	11	14
Picked	3	2	5
Done	0	6	6
Total	1282	34	1316

Accuracy

100.0%

Counts

1316 → 34

Alt Table

Click to see full alt table

Status	Accuracy	Program
	53.4%	(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
	52.2%	(/.f64 (/.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x))
	51.8%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
✓	53.5%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
	75.4%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) x)) x)
	52.2%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
	53.4%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
✓	53.3%	(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
	45.5%	(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
✓	52.3%	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
	25.0%	(/.f64 (+.f64 #s(literal 120 binary64) (/.f64 #s(literal -2400 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
	26.4%	(/.f64 #s(literal 120 binary64) (.f64 x (.f64 x (*.f64 x x))))
	29.3%	(/.f64 #s(literal 6 binary64) (*.f64 x x))
	50.3%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
	51.9%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 4 binary64)) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))
	51.8%	(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
	50.3%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))))
	53.0%	(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
	75.6%	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))
	72.8%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal 1/3024 binary64))))))))
	53.0%	(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
	50.3%	(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))))
✓	52.3%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
	26.6%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))))
	29.3%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
	52.2%	(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (cos.f64 x) (*.f64 x x)))
	52.1%	(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
	49.7%	(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
✓	49.2%	(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
✓	76.0%	(*.f64 (/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
✓	76.0%	(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
	51.8%	(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
	50.3%	(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))
✓	50.3%	#s(literal 1/2 binary64)

Compiler

Compiled 1374 to 530 computations (61.4% saved)

regimes56.0ms (0.3%)

Counts

57 → 2

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) x) x)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))
(/.f64 #s(literal 120 binary64) (.f64 x (.f64 x (*.f64 x x))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) x)) x)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))))
(/.f64 (+.f64 #s(literal 120 binary64) (/.f64 #s(literal -2400 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x #s(literal 1/3024 binary64)))))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal 1/3024 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 4 binary64)) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (+.f64 (cos.f64 x) #s(literal -1 binary64)) x))
(.f64 (/.f64 #s(literal -1 binary64) (.f64 x x)) (+.f64 (cos.f64 x) #s(literal -1 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (cos.f64 x) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
(-.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (/.f64 (cos.f64 x) x) x))
(-.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (cos.f64 x) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (-.f64 x (.f64 x (cos.f64 x))) (.f64 x (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x))))
(/.f64 (/.f64 (-.f64 x (.f64 x (cos.f64 x))) x) (.f64 x x))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (cos.f64 x)))) x)
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x (.f64 x x)) (-.f64 x (*.f64 x (cos.f64 x)))))
(+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 0 binary64) (cos.f64 x))))
(-.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 (cos.f64 x) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))))
(/.f64 (.f64 (.f64 x x) (+.f64 (cos.f64 x) #s(literal -1 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))
(/.f64 (/.f64 (-.f64 (.f64 x x) (.f64 x (.f64 x (cos.f64 x)))) (.f64 x x)) (*.f64 x x))
(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (cos.f64 x))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
(.f64 (/.f64 (sin.f64 x) (.f64 x x)) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(*.f64 (/.f64 (sin.f64 x) (/.f64 x (/.f64 #s(literal 1 binary64) x))) (tan.f64 (/.f64 x #s(literal 2 binary64))))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x) (/.f64 (-.f64 #s(literal 0 binary64) (cos.f64 x)) (*.f64 x x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (cos.f64 x)))))
(/.f64 (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64)) (.f64 x x)) (+.f64 #s(literal 1 binary64) (cos.f64 x)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 (.f64 x #s(literal 2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal -1 binary64) (*.f64 x x))) (+.f64 #s(literal 1 binary64) (cos.f64 x)))

Outputs
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x)

Calls

2 calls:

23.0ms	(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))
23.0ms	x

Results

Accuracy	Segments	Branch
99.7%	2	`x`
98.0%	2	`(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))`

Compiler

Compiled 11 to 7 computations (36.4% saved)

regimes24.0ms (0.1%)

Counts

27 → 2

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) x) x)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))
(/.f64 #s(literal 120 binary64) (.f64 x (.f64 x (*.f64 x x))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) x)) x)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))))
(/.f64 (+.f64 #s(literal 120 binary64) (/.f64 #s(literal -2400 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x #s(literal 1/3024 binary64)))))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal 1/3024 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 4 binary64)) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Outputs
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x))

Calls

1 calls:

12.0ms

Results

Accuracy	Segments	Branch
99.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes15.0ms (0.1%)

Counts

26 → 1

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) x) x)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))
(/.f64 #s(literal 120 binary64) (.f64 x (.f64 x (*.f64 x x))))
(+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64)))))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) #s(literal 1/120 binary64))))))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))) x)) x)
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal 1/120 binary64))) #s(literal 1/6 binary64)))))
(/.f64 (+.f64 #s(literal 120 binary64) (/.f64 #s(literal -2400 binary64) (.f64 x x))) (.f64 x (.f64 x (.f64 x x))))
(/.f64 (.f64 #s(literal -1/2 binary64) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (*.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 x (.f64 x #s(literal 1/3024 binary64)))))))))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/6 binary64) (.f64 (.f64 x x) (+.f64 #s(literal 1/120 binary64) (.f64 (.f64 x x) #s(literal 1/3024 binary64))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 4 binary64) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))) #s(literal 4 binary64)) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))
(/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 x x)) #s(literal -1 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x)))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (*.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64))))))
(/.f64 #s(literal 1 binary64) (.f64 (+.f64 #s(literal 8 binary64) (.f64 #s(literal 1/216 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 4 binary64) (.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) (-.f64 (.f64 x (.f64 x #s(literal 1/6 binary64))) #s(literal 2 binary64)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 #s(literal 4 binary64) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x)))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (.f64 #s(literal 1/36 binary64) (.f64 (.f64 x x) (.f64 x x))))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (.f64 x x))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/6 binary64) (*.f64 x x))))))

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

Calls

1 calls:

11.0ms

Results

Accuracy	Segments	Branch
75.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0%)

Counts

7 → 2

Calls

Call 1

Inputs
#s(literal 1/2 binary64)
(/.f64 #s(literal 6 binary64) (*.f64 x x))
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x #s(literal 1/6 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) (*.f64 x x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 2 binary64) x)) x)
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) #s(literal 1 binary64)) x) x)

Outputs
(+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x)))
(/.f64 #s(literal 6 binary64) (*.f64 x x))

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
75.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

2 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
75.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 1/2 binary64)

Outputs
#s(literal 1/2 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
50.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch34.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
30.0ms	0.005890757415762508	7.041633526927786

Results

18.0ms

128×

valid

Compiler

Compiled 213 to 145 computations (31.9% saved)

Precisions

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

ival-mult: 5.0ms (41.6% of total)

ival-cos: 3.0ms (25% of total)

ival-sub: 2.0ms (16.7% of total)

ival-div: 2.0ms (16.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch30.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
27.0ms	0.005890757415762508	7.041633526927786

Results

15.0ms

128×

valid

Compiler

Compiled 213 to 145 computations (31.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 9.0ms

ival-cos: 3.0ms (33.4% of total)

ival-sub: 2.0ms (22.2% of total)

ival-div: 2.0ms (22.2% of total)

ival-mult: 2.0ms (22.2% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch39.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
36.0ms	0.005890757415762508	7.041633526927786

Results

24.0ms

128×

valid

Compiler

Compiled 141 to 105 computations (25.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-cos: 12.0ms (64.9% of total)

ival-sub: 2.0ms (10.8% of total)

ival-div: 2.0ms (10.8% of total)

ival-mult: 2.0ms (10.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

bsearch35.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
32.0ms	0.005890757415762508	7.041633526927786

Results

20.0ms

128×

valid

Compiler

Compiled 93 to 73 computations (21.5% saved)

Precisions

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

ival-cos: 8.0ms (56.1% of total)

ival-sub: 2.0ms (14% of total)

ival-div: 2.0ms (14% of total)

ival-mult: 2.0ms (14% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

simplify23.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	86
1	47	86
2	51	86
3	53	86
4	54	86

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 x #s(literal 8070450532247929/288230376151711744 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 8070450532247929/288230376151711744 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 7/2 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
#s(literal 1/2 binary64)

Outputs
(if (<=.f64 x #s(literal 8070450532247929/288230376151711744 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))) (/.f64 (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) x) x))
(if (<=.f64 x #s(literal 8070450532247929/288230376151711744 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/24 binary64) (.f64 (.f64 x x) #s(literal 1/720 binary64))))) (/.f64 (-.f64 #s(literal 1 binary64) (cos.f64 x)) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 2 binary64) (.f64 (.f64 x x) #s(literal 1/6 binary64))))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal -1/24 binary64) (.f64 x x))) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 3602879701896397/1125899906842624 binary64)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x x) #s(literal -1/24 binary64))) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 7/2 binary64)) #s(literal 1/2 binary64) (/.f64 #s(literal 6 binary64) (*.f64 x x)))
#s(literal 1/2 binary64)

soundness2.5s (13%)

Rules

3404×	`/-lowering-/.f32`
3404×	`/-lowering-/.f64`
3146×	`-lowering-.f32`
3146×	`-lowering-.f64`
2724×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	42	278
1	113	266
2	315	266
3	818	266
4	1931	266
5	2941	266
6	3513	266
7	4835	266
0	8655	266
0	148	1621
1	396	1547
2	1059	1543
3	2805	1531
4	5463	1531
0	8184	1531
0	146	1695
1	428	1626
2	1210	1603
3	3670	1594
4	5156	1594
5	7979	1594
0	8159	1594
0	22	102
1	162	94
2	1666	91
0	9177	91

Stop Event

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

Compiler

Compiled 250 to 145 computations (42% saved)

preprocess182.0ms (0.9%)

Compiler: Compiled 244 to 114 computations (53.3% saved)

analyze4.0ms (0%)

sample3.1s (15.9%)

preprocess234.0ms (1.2%)

explain273.0ms (1.4%)

eval1.0ms (0%)

prune2.0ms (0%)

simplify144.0ms (0.7%)

localize206.0ms (1.1%)

series7.0ms (0%)

rewrite710.0ms (3.7%)

simplify475.0ms (2.5%)

eval210.0ms (1.1%)

prune177.0ms (0.9%)

simplify330.0ms (1.7%)

localize514.0ms (2.7%)

series35.0ms (0.2%)

rewrite1000.0ms (5.2%)

simplify900.0ms (4.6%)

eval663.0ms (3.4%)

prune477.0ms (2.5%)

simplify393.0ms (2%)

localize717.0ms (3.7%)

series27.0ms (0.1%)

rewrite828.0ms (4.3%)

simplify619.0ms (3.2%)

eval504.0ms (2.6%)

prune604.0ms (3.1%)

simplify404.0ms (2.1%)

localize641.0ms (3.3%)

series40.0ms (0.2%)

rewrite922.0ms (4.8%)

simplify544.0ms (2.8%)

eval412.0ms (2.1%)

prune306.0ms (1.6%)

regimes56.0ms (0.3%)

regimes24.0ms (0.1%)

regimes15.0ms (0.1%)

regimes6.0ms (0%)

regimes3.0ms (0%)

regimes3.0ms (0%)

bsearch34.0ms (0.2%)

bsearch30.0ms (0.2%)

bsearch39.0ms (0.2%)

bsearch35.0ms (0.2%)

simplify23.0ms (0.1%)

soundness2.5s (13%)

preprocess182.0ms (0.9%)

end0.0ms (0%)

Profiling