Details

analyze264.0ms (4%)

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
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
37.5%	37.5%	62.5%	0%	0%	0%	0%	4
43.8%	43.7%	56.2%	0%	0%	0%	0%	5
46.9%	46.9%	53.1%	0%	0%	0%	0%	6
48.4%	48.4%	51.5%	0%	0%	0%	0%	7
49.2%	49.2%	50.8%	0%	0%	0%	0%	8
49.6%	49.6%	50.4%	0%	0%	0%	0%	9
49.8%	49.8%	50.2%	0%	0%	0%	0%	10
49.9%	49.9%	50.1%	0%	0%	0%	0%	11
50%	49.9%	50%	0%	0%	0%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample5.9s (88.1%)

Results

3.1s	2088×	body	2048	valid
1.8s	3082×	body	1024	valid
544.0ms	1557×	body	512	valid
289.0ms	1424×	body	256	valid
149.0ms	104×	body	4096	valid
2.0ms	1×	body	8192	valid

Bogosity

preprocess24.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

145×	`fma-def_binary64`
111×	`fma-neg_binary64`
30×	`cancel-sign-sub-inv_binary64`
27×	`div-sub_binary64`
21×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	17	6
2	23	6
3	33	6
4	56	6
5	79	6
6	116	6
7	185	6
8	336	6
9	537	6
10	685	6
11	719	6
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

145×	`fma-def_binary64`
111×	`fma-neg_binary64`
30×	`cancel-sign-sub-inv_binary64`
27×	`div-sub_binary64`
21×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	17	6
2	23	6
3	33	6
4	56	6
5	79	6
6	116	6
7	185	6
8	336	6
9	537	6
10	685	6
11	719	6

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

Outputs
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(tan.f64 (/.f64 x 2))

eval1.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 5 to 4 computations (20% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 10 to 7 computations (30% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(tan.f64 (/.f64 x 2))
1.0ms	x	@	inf	(tan.f64 (/.f64 x 2))
1.0ms	x	@	-inf	(tan.f64 (/.f64 x 2))

rewrite36.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`pow1_binary64`
500×	`add-sqr-sqrt_binary64`
475×	`add-log-exp_binary64`
475×	`log1p-expm1-u_binary64`
475×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	110	6
2	1290	6

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(tan.f64 (/.f64 x 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (tan.f64 (.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (tan.f64 (.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (tan.f64 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (neg.f64 (cos.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tan.f64 (.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (tan.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cos.f64 (*.f64 x 1/2)) (sin.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 (*.f64 x 1/2)) (cos.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (neg.f64 (cos.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tan.f64 (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))))))

simplify49.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

529×	`log-prod_binary64`
510×	`fma-neg_binary64`
396×	`fma-def_binary64`
371×	`exp-prod_binary64`
244×	`exp-sum_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	418
1	143	370
2	437	322
3	2067	322
4	4566	322
5	6579	322

Stop Event

1×	node limit

Counts

32 → 37

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(/.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (neg.f64 (cos.f64 (.f64 x 1/2))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(.f64 x (fma.f64 x (.f64 x 1/24) 1/2))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/2 x)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 17/40320 (pow.f64 x 7)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (neg.f64 (cos.f64 (.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))

eval10.0ms (0.1%)

Compiler: Compiled 358 to 288 computations (19.6% saved)

prune5.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	35	2	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	35	3	38

Error

Counts

38 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
▶	31.9b	(*.f64 1/2 x)
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 19 to 15 computations (21.1% saved)

localize3.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

localize13.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

Compiler

Compiled 23 to 17 computations (26.1% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
0.0ms	x	@	-inf	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
0.0ms	x	@	inf	(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

rewrite39.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

724×	`pow1_binary64`
669×	`add-log-exp_binary64`
669×	`log1p-expm1-u_binary64`
669×	`expm1-log1p-u_binary64`
655×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	145	6
2	1778	6

Stop Event

1×	node limit

Counts

1 → 32

Calls

Call 1

Inputs
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (tan.f64 (.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (tan.f64 (.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (tan.f64 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (neg.f64 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (cos.f64 (.f64 x 1/2))) (sin.f64 (.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tan.f64 (.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tan.f64 (.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x tan.f64 (*.f64 x 1/2))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (tan.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (*.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (*.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sin.f64 (*.f64 x 1/2))) (/.f64 1 (neg.f64 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cos.f64 (*.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (cos.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (*.f64 x 1/2))) 2)) (/.f64 (sin.f64 (*.f64 x 1/2)) (cbrt.f64 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (pow.f64 (cbrt.f64 (cos.f64 (*.f64 x 1/2))) 2)) (/.f64 (sqrt.f64 (sin.f64 (*.f64 x 1/2))) (cbrt.f64 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (cos.f64 (*.f64 x 1/2)))) (/.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) 2) (sqrt.f64 (cos.f64 (*.f64 x 1/2)))) (/.f64 (cbrt.f64 (sin.f64 (*.f64 x 1/2))) (sqrt.f64 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tan.f64 (*.f64 x 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (neg.f64 (cos.f64 (*.f64 x 1/2)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (sin.f64 (*.f64 x 1/2)) 3) (pow.f64 (cos.f64 (*.f64 x 1/2)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x tan.f64 (*.f64 x 1/2))))))

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

461×	`fma-def_binary64`
395×	`log-prod_binary64`
377×	`fma-neg_binary64`
297×	`associate-l_binary64`
267×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	610
1	252	556
2	739	502
3	3569	499
4	6917	499

Stop Event

1×	node limit

Counts

44 → 49

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (neg.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 1 (cos.f64 (.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (cos.f64 (.f64 x 1/2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (.f64 x 1/2))))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (cos.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 1 (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (cos.f64 (.f64 x 1/2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (cos.f64 (*.f64 x 1/2)))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(neg.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2)))))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 x 1/2))

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (fma.f64 1/240 (pow.f64 x 5) (*.f64 17/40320 (pow.f64 x 7)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(-.f64 (+.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (cbrt.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (cos.f64 (*.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (/.f64 1 (neg.f64 (cos.f64 (*.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 1 (cos.f64 (.f64 x 1/2))) (sin.f64 (*.f64 x 1/2)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) 1) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) 1) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cos.f64 (.f64 x 1/2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 1 (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (cos.f64 (.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (cbrt.f64 (tan.f64 (.f64 x 1/2))))
(.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2)))
(.f64 (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (cos.f64 (.f64 x 1/2))) 2)) (/.f64 (sqrt.f64 (sin.f64 (.f64 x 1/2))) (cbrt.f64 (cos.f64 (*.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 1 (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 (cos.f64 (.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) 2) (sqrt.f64 (cos.f64 (.f64 x 1/2)))) (/.f64 (cbrt.f64 (sin.f64 (.f64 x 1/2))) (sqrt.f64 (cos.f64 (*.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(neg.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (neg.f64 (cos.f64 (.f64 x 1/2)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 x 1/2)) 3) (pow.f64 (cos.f64 (.f64 x 1/2)) 3)))
(cbrt.f64 (/.f64 (pow.f64 (sin.f64 (.f64 1/2 x)) 3) (pow.f64 (cos.f64 (.f64 1/2 x)) 3)))
(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(tan.f64 (*.f64 x 1/2))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))

eval15.0ms (0.2%)

Compiler: Compiled 591 to 489 computations (17.3% saved)

prune7.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	49	3	52

Error

Counts

52 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.3b	(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
✓	31.9b	(*.f64 1/2 x)
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(tan.f64 (*.f64 1/2 x))
✓	0.2b	(-.f64 (tan.f64 (*.f64 1/2 x)) 1)
✓	1.8b	(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))

Compiler

Compiled 25 to 20 computations (20% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(-.f64 (tan.f64 (*.f64 1/2 x)) 1)
0.0ms	x	@	0	(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
0.0ms	x	@	inf	(-.f64 (tan.f64 (*.f64 1/2 x)) 1)
0.0ms	x	@	-inf	(-.f64 (tan.f64 (*.f64 1/2 x)) 1)
0.0ms	x	@	inf	(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))

rewrite55.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

821×	`pow1_binary64`
766×	`add-log-exp_binary64`
765×	`log1p-expm1-u_binary64`
765×	`expm1-log1p-u_binary64`
754×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	33
1	178	21
2	2345	21

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

Inputs
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(-.f64 (tan.f64 (*.f64 1/2 x)) 1)
(tan.f64 (*.f64 1/2 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (tan.f64 (*.f64 1/2 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)) (/.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (tan.f64 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3)) (/.f64 1 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2)) (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1)) (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1) (-.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3)) (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3)) (+.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2)) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 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(#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tan.f64 (*.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x tan.f64 (*.f64 1/2 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 2) (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (tan.f64 (*.f64 1/2 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (tan.f64 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 2) (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (*.f64 1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) -1) (/.f64 1 (+.f64 1 (tan.f64 (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 1) (-.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (*.f64 1/2 x)))) (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) -1) (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) -1) (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) (-.f64 1 (*.f64 (tan.f64 (*.f64 1/2 x)) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) -1) (+.f64 1 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) -1) (-.f64 (tan.f64 (*.f64 1/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (*.f64 1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2) -1)) (neg.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (tan.f64 (*.f64 1/2 x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))) -1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (tan.f64 (*.f64 1/2 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (tan.f64 (*.f64 1/2 x)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)) (/.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (tan.f64 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (tan.f64 (*.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2) (*.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) (*.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sin.f64 (*.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3)) (/.f64 1 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2)) (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (cos.f64 (*.f64 1/2 x)) (sin.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1)) (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1) (-.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sin.f64 (*.f64 1/2 x)) (cos.f64 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3)) (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3)) (+.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2)) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (sin.f64 (*.f64 1/2 x))) (neg.f64 (cos.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))) (neg.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2))) (neg.f64 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 3) 1) (+.f64 (*.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) (+.f64 1 (tan.f64 (*.f64 1/2 x)))) (+.f64 1 (+.f64 1 (tan.f64 (*.f64 1/2 x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) (+.f64 1 (tan.f64 (*.f64 1/2 x)))) 1) (+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2) 1) (-.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (sin.f64 (*.f64 1/2 x)) 1) (cos.f64 (*.f64 1/2 x)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (tan.f64 (*.f64 1/2 x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 2) (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 1)))))

simplify55.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

632×	`distribute-rgt-in_binary64`
540×	`distribute-lft-in_binary64`
523×	`fma-neg_binary64`
408×	`cancel-sign-sub-inv_binary64`
383×	`times-frac_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	177	2411
1	413	2283
2	1627	2261

Stop Event

1×	node limit

Counts

152 → 114

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
-1
(-.f64 (*.f64 1/2 x) 1)
(-.f64 (+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3))) 1)
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3)))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(-.f64 (tan.f64 (*.f64 1/2 x)) 0)
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(-.f64 (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1)) (/.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(.f64 1 (tan.f64 (.f64 1/2 x)))
(.f64 (tan.f64 (.f64 1/2 x)) 1)
(.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 2) (.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 1))
(.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) 1))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (/.f64 1 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (.f64 1/2 x))) 1))))
(.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2)) (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 1 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (.f64 1/2 x))) 1)) (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))))
(/.f64 1 (/.f64 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1) (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (+.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2)) (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1))
(/.f64 (neg.f64 (sin.f64 (.f64 1/2 x))) (neg.f64 (cos.f64 (.f64 1/2 x))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3))) (neg.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2))) (neg.f64 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1)))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 3) 1) (+.f64 (.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x)))) (+.f64 1 (+.f64 1 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (-.f64 (.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x)))) 1) (+.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 1))
(/.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) 1) (-.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 1))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) 1) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(fma.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 2) (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 1)
(fma.f64 (sqrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) (sqrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 1)
(+.f64 (tan.f64 (*.f64 1/2 x)) -1)
(+.f64 -1 (tan.f64 (*.f64 1/2 x)))
(.f64 1 (+.f64 (tan.f64 (.f64 1/2 x)) -1))
(.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 1)
(.f64 (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 2))
(.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 2) (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))
(.f64 (sqrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))
(.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 3) -1) (/.f64 1 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (.f64 1/2 x))))))
(.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) -1) (/.f64 1 (+.f64 1 (tan.f64 (*.f64 1/2 x)))))
(.f64 (+.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) 1) (-.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 1))
(/.f64 1 (/.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (.f64 1/2 x)))) (+.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) -1)))
(/.f64 1 (/.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) -1)))
(/.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 3) -1) (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (*.f64 1/2 x)))))
(/.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 3) -1) (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) (-.f64 1 (.f64 (tan.f64 (.f64 1/2 x)) -1))))
(/.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) -1) (+.f64 1 (tan.f64 (.f64 1/2 x))))
(/.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) -1) (-.f64 (tan.f64 (.f64 1/2 x)) -1))
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 3) -1)) (neg.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) (+.f64 1 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) 2) -1)) (neg.f64 (+.f64 1 (tan.f64 (.f64 1/2 x)))))
(pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)
(pow.f64 (cbrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 3)
(pow.f64 (sqrt.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)) 2)
(pow.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3) 1/3)
(sqrt.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 2))
(log.f64 (exp.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))
(cbrt.f64 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))
(expm1.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(log1p.f64 (expm1.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))
(exp.f64 (log.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1)))
(fma.f64 1 (tan.f64 (*.f64 1/2 x)) -1)
(fma.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (.f64 1/2 x))) -1)
(fma.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (sqrt.f64 (tan.f64 (.f64 1/2 x))) -1)
(+.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1))
(+.f64 (tan.f64 (*.f64 1/2 x)) 0)
(+.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)
(+.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) -1)
(-.f64 (tan.f64 (*.f64 1/2 x)) 0)
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(-.f64 (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1)) (/.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(.f64 1 (tan.f64 (.f64 1/2 x)))
(.f64 (tan.f64 (.f64 1/2 x)) 1)
(.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 2) (.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 1))
(.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) 1))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (/.f64 1 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (.f64 1/2 x))) 1))))
(.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2)) (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 1 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (.f64 1/2 x))) 1)) (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))))
(/.f64 1 (/.f64 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1) (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (+.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2)) (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1))
(/.f64 (neg.f64 (sin.f64 (.f64 1/2 x))) (neg.f64 (cos.f64 (.f64 1/2 x))))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3))) (neg.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1))))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2))) (neg.f64 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1)))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 3) 1) (+.f64 (.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x)))) (+.f64 1 (+.f64 1 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (-.f64 (.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x)))) 1) (+.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 1))
(/.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) 1) (-.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 1))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) 1) (cos.f64 (*.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(fma.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 2) (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 1)
(fma.f64 (sqrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) (sqrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 1)

Outputs
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
-1
(-.f64 (*.f64 1/2 x) 1)
(fma.f64 1/2 x -1)
(-.f64 (+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3))) 1)
(+.f64 (fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3))) -1)
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) -1))
(-.f64 (+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3)))) 1)
(+.f64 (fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3)))) -1)
(+.f64 (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))) (fma.f64 1/2 x -1))
(+.f64 (fma.f64 1/2 x (*.f64 1/240 (pow.f64 x 5))) (fma.f64 1/24 (pow.f64 x 3) -1))
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(-.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) 1)
(+.f64 (/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x))) -1)
(*.f64 1/2 x)
(+.f64 (.f64 1/2 x) (.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/2 x (*.f64 1/24 (pow.f64 x 3)))
(fma.f64 1/24 (pow.f64 x 3) (*.f64 1/2 x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (*.f64 1/24 (pow.f64 x 3))))
(fma.f64 1/2 x (fma.f64 1/24 (pow.f64 x 3) (*.f64 1/240 (pow.f64 x 5))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/240 (pow.f64 x 5)) (+.f64 (.f64 17/40320 (pow.f64 x 7)) (.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 17/40320 (pow.f64 x 7) (*.f64 1/24 (pow.f64 x 3)))))
(fma.f64 1/2 x (fma.f64 1/240 (pow.f64 x 5) (fma.f64 1/24 (pow.f64 x 3) (*.f64 17/40320 (pow.f64 x 7)))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(-.f64 (tan.f64 (*.f64 1/2 x)) 0)
(tan.f64 (*.f64 1/2 x))
(-.f64 (+.f64 1 (tan.f64 (*.f64 1/2 x))) 1)
(tan.f64 (*.f64 1/2 x))
(-.f64 (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1)) (/.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 1 (-.f64 (tan.f64 (.f64 1/2 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 2 (tan.f64 (.f64 1/2 x))))
(.f64 1 (tan.f64 (.f64 1/2 x)))
(tan.f64 (*.f64 1/2 x))
(.f64 (tan.f64 (.f64 1/2 x)) 1)
(tan.f64 (*.f64 1/2 x))
(.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 2))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 2) (cbrt.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 2) (.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) 1))
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (sqrt.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) 1))
(tan.f64 (*.f64 1/2 x))
(.f64 (sin.f64 (.f64 1/2 x)) (/.f64 1 (cos.f64 (*.f64 1/2 x))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (/.f64 1 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (.f64 1/2 x))) 1))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2) (tan.f64 (.f64 1/2 x))))) (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 3)) (+.f64 (-.f64 2 (tan.f64 (.f64 1/2 x))) (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 2)))
(.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2)) (/.f64 1 (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 1 (-.f64 (tan.f64 (.f64 1/2 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 2 (tan.f64 (.f64 1/2 x))))
(/.f64 1 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (.f64 1/2 x))) 1)) (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2) (tan.f64 (.f64 1/2 x))))) (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 3)) (+.f64 (-.f64 2 (tan.f64 (.f64 1/2 x))) (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 2)))
(/.f64 1 (/.f64 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1) (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 1 (-.f64 (tan.f64 (.f64 1/2 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 2 (tan.f64 (.f64 1/2 x))))
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(/.f64 1 (/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (.f64 1/2 x))) 1)) (+.f64 1 (pow.f64 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 3))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2) (tan.f64 (.f64 1/2 x))))) (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 3)) (+.f64 (-.f64 2 (tan.f64 (.f64 1/2 x))) (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 2)))
(/.f64 1 (/.f64 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1) (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2))))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 1 (-.f64 (tan.f64 (.f64 1/2 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 2 (tan.f64 (.f64 1/2 x))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2) (tan.f64 (.f64 1/2 x))))) (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 3)) (+.f64 (-.f64 2 (tan.f64 (.f64 1/2 x))) (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 2)))
(/.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3)) (+.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (+.f64 (-.f64 1 (tan.f64 (*.f64 1/2 x))) 1)))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2) (tan.f64 (.f64 1/2 x))))) (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 3)) (+.f64 (-.f64 2 (tan.f64 (.f64 1/2 x))) (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 2)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2)) (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 1 (-.f64 (tan.f64 (.f64 1/2 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 2 (tan.f64 (.f64 1/2 x))))
(/.f64 (neg.f64 (sin.f64 (.f64 1/2 x))) (neg.f64 (cos.f64 (.f64 1/2 x))))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(/.f64 (neg.f64 (+.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 3))) (neg.f64 (+.f64 1 (+.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) (tan.f64 (*.f64 1/2 x))) 1))))
(/.f64 1 (/.f64 (+.f64 1 (+.f64 1 (-.f64 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2) (tan.f64 (.f64 1/2 x))))) (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 3))))
(/.f64 (+.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 3)) (+.f64 (-.f64 2 (tan.f64 (.f64 1/2 x))) (pow.f64 (+.f64 -1 (tan.f64 (*.f64 1/2 x))) 2)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2))) (neg.f64 (+.f64 (-.f64 1 (tan.f64 (.f64 1/2 x))) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 1 (-.f64 (tan.f64 (.f64 1/2 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 2 (tan.f64 (.f64 1/2 x))))
(/.f64 (-.f64 (pow.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 3) 1) (+.f64 (.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x)))) (+.f64 1 (+.f64 1 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (+.f64 (pow.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 3) -1) (fma.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 2 (tan.f64 (.f64 1/2 x)))))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 3)) (fma.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 (tan.f64 (.f64 1/2 x)) 2)))
(/.f64 (+.f64 -1 (pow.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 3)) (+.f64 1 (.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 (tan.f64 (.f64 1/2 x)) 2))))
(/.f64 (-.f64 (.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) (+.f64 1 (tan.f64 (.f64 1/2 x)))) 1) (+.f64 (+.f64 1 (tan.f64 (.f64 1/2 x))) 1))
(/.f64 (.f64 (+.f64 2 (tan.f64 (.f64 1/2 x))) (tan.f64 (.f64 1/2 x))) (+.f64 2 (tan.f64 (.f64 1/2 x))))
(/.f64 (.f64 (tan.f64 (.f64 1/2 x)) (+.f64 (tan.f64 (.f64 1/2 x)) 2)) (+.f64 (tan.f64 (.f64 1/2 x)) 2))
(.f64 (/.f64 (+.f64 (tan.f64 (.f64 1/2 x)) 2) (+.f64 (tan.f64 (.f64 1/2 x)) 2)) (tan.f64 (.f64 1/2 x)))
(/.f64 (-.f64 (pow.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 2) 1) (-.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1) 1))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 1 (-.f64 (tan.f64 (.f64 1/2 x)) 1)))
(/.f64 (-.f64 1 (pow.f64 (+.f64 -1 (tan.f64 (.f64 1/2 x))) 2)) (-.f64 2 (tan.f64 (.f64 1/2 x))))
(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) 1) (cos.f64 (*.f64 1/2 x)))
(/.f64 (sin.f64 (.f64 1/2 x)) (cos.f64 (.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 1/2 x)) 1)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 1/2 x))) 3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 1/2 x))) 2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3) 1/3)
(tan.f64 (*.f64 1/2 x))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 2))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) 3))
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 1/2 x))))
(tan.f64 (*.f64 1/2 x))
(fma.f64 1 (+.f64 (tan.f64 (*.f64 1/2 x)) -1) 1)
(tan.f64 (*.f64 1/2 x))
(fma.f64 (pow.f64 (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 2) (cbrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 1)
(tan.f64 (*.f64 1/2 x))
(fma.f64 (sqrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) (sqrt.f64 (+.f64 (tan.f64 (.f64 1/2 x)) -1)) 1)
(tan.f64 (*.f64 1/2 x))

eval43.0ms (0.6%)

Compiler: Compiled 1738 to 1510 computations (13.1% saved)

prune15.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	113	4	117

Error

Counts

117 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.3b	(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
▶	61.2b	(+.f64 1 -1)
✓	31.9b	(*.f64 1/2 x)
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 22 to 19 computations (13.6% saved)

localize2.0ms (0%)

Compiler: Compiled 6 to 6 computations (0% saved)

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	3	3
Total	4	4

Error

Counts

4 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	29.3b	(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
✓	61.2b	(+.f64 1 -1)
✓	31.9b	(*.f64 1/2 x)
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 22 to 19 computations (13.6% saved)

regimes15.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 1 -1)
(tan.f64 (/.f64 x 2))
(+.f64 1 (-.f64 (tan.f64 (*.f64 1/2 x)) 1))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

Outputs
(tan.f64 (/.f64 x 2))

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
4.0ms	x

Results

Error	Segments	Branch
0.0b	1	`x`
0.0b	1	`(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))`

Compiler

Compiled 45 to 35 computations (22.2% saved)

regimes4.0ms (0.1%)

Accuracy

Total -29.6b remaining (-92.7%)

Threshold costs -29.6b (-92.7%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(+.f64 1 -1)

Outputs
(*.f64 1/2 x)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
31.9b	1	`x`

Compiler

Compiled 9 to 7 computations (22.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)

Outputs
(tan.f64 (/.f64 x 2))
(*.f64 1/2 x)
(*.f64 x 1/2)

Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness26.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

145×	`fma-def_binary64`
111×	`fma-neg_binary64`
30×	`cancel-sign-sub-inv_binary64`
27×	`div-sub_binary64`
21×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	17	6
2	23	6
3	33	6
4	56	6
5	79	6
6	116	6
7	185	6
8	336	6
9	537	6
10	685	6
11	719	6

Stop Event

1×

saturated

Compiler

Compiled 13 to 10 computations (23.1% saved)

end17.0ms (0.3%)

Compiler: Compiled 8 to 6 computations (25% saved)

Details

analyze264.0ms (4%)

sample5.9s (88.1%)

preprocess24.0ms (0.4%)

simplify16.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite36.0ms (0.5%)

simplify49.0ms (0.7%)

eval10.0ms (0.1%)

prune5.0ms (0.1%)

localize3.0ms (0%)

localize13.0ms (0.2%)

series1.0ms (0%)

rewrite39.0ms (0.6%)

simplify50.0ms (0.7%)

eval15.0ms (0.2%)

prune7.0ms (0.1%)

localize13.0ms (0.2%)

series3.0ms (0%)

rewrite55.0ms (0.8%)

simplify55.0ms (0.8%)

eval43.0ms (0.6%)

prune15.0ms (0.2%)

localize2.0ms (0%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes15.0ms (0.2%)

regimes4.0ms (0.1%)

simplify2.0ms (0%)

soundness26.0ms (0.4%)

end17.0ms (0.3%)

Profiling