Details

analyze282.0ms (3.6%)

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)

sample6.4s (81.7%)

Results

3.6s	2114×	body	2048	valid
1.7s	3071×	body	1024	valid
699.0ms	1523×	body	512	valid
264.0ms	1457×	body	256	valid
95.0ms	90×	body	4096	valid
2.0ms	1×	body	8192	valid

Bogosity

preprocess51.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

196×	`fma-def`
118×	`associate-r`
90×	`*-commutative`
80×	`associate-+l-`
74×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11
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)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

196×	`fma-def`
118×	`associate-r`
90×	`*-commutative`
80×	`associate-+l-`
74×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11

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))

eval0.0ms (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)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite77.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1392×	`add-sqr-sqrt`
1366×	`*-un-lft-identity`
1276×	`add-cube-cbrt`
1264×	`add-cbrt-cube`
1250×	`add-exp-log`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	148	11
2	1723	11

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

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

854×	`associate-*r/`
720×	`fma-def`
682×	`*-commutative`
650×	`associate-r`
574×	`associate-*l/`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	68	804
1	147	708
2	524	612
3	2040	612
4	4521	612
5	6576	612

Stop Event

1×	node limit

Counts

32 → 36

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 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (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 (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 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(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))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(log1p.f64 (expm1.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 (.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 1 (-.f64 (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 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 (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 (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 (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 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 (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 (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))
(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))
(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))
(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))
(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))

eval37.0ms (0.5%)

Compiler: Compiled 350 to 283 computations (19.1% saved)

prune5.0ms (0.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	34	3	37

Error

0.0b

Counts

37 → 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)))
▶	29.8b	(*.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)

localize48.0ms (0.6%)

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)

series0.0ms (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)))

rewrite88.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1814×	`add-sqr-sqrt`
1796×	`*-un-lft-identity`
1668×	`add-cube-cbrt`
1648×	`add-cbrt-cube`
182×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	183	11
2	2215	11

Stop Event

1×	node limit

Counts

1 → 33

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

Outputs

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

simplify50.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1216×	`associate-/r/`
956×	`associate-r`
902×	`distribute-rgt-in`
892×	`distribute-lft-in`
814×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	106	939
1	251	939
2	857	939
3	3771	939

Stop Event

1×	node limit

Counts

45 → 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 (exp.f64 (log1p.f64 (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 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.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 (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 (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 (/.f64 1 (cos.f64 (.f64 x 1/2))) (sin.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 (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 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 (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 (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 (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 (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 (/.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))))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(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))))
(log.f64 (+.f64 1 (expm1.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))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) 1))
(tan.f64 (*.f64 x 1/2))
(log1p.f64 (expm1.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 (.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 1/2 x (*.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 (exp.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2)))) 1)
(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)
(tan.f64 (*.f64 1/2 x))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(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 (cbrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 2))
(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))))
(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 (/.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 (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 (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 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 (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 (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 (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 (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)))
(.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 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (cbrt.f64 (sin.f64 (.f64 1/2 x))) 2)) (pow.f64 (cbrt.f64 (cos.f64 (.f64 1/2 x))) 2))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(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))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(log.f64 (+.f64 1 (expm1.f64 (tan.f64 (*.f64 x 1/2)))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) 1))
(tan.f64 (*.f64 1/2 x))
(tan.f64 (*.f64 x 1/2))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))

eval52.0ms (0.7%)

Compiler: Compiled 595 to 491 computations (17.5% saved)

prune6.0ms (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

0.0b

Counts

52 → 3

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
✓	29.8b	(*.f64 1/2 x)
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 26 to 21 computations (19.2% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
1.0ms	x	@	-inf	(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
0.0ms	x	@	0	(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
0.0ms	x	@	0	(/.f64 1 (tan.f64 (*.f64 x 1/2)))
0.0ms	x	@	inf	(/.f64 1 (tan.f64 (*.f64 x 1/2)))

rewrite63.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

1740×	`add-sqr-sqrt`
1712×	`*-un-lft-identity`
1592×	`add-cube-cbrt`
1578×	`add-cbrt-cube`
200×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	63
1	223	39
2	2466	39

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

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

Outputs

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

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

simplify112.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

1004×	`associate-*r/`
932×	`associate-+r+`
884×	`associate-/r*`
686×	`associate-+l+`
630×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	153	2547
1	343	2459
2	1384	2459
3	6159	2459

Stop Event

1×	node limit

Counts

125 → 94

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 2 x)
(+.f64 (.f64 -1/6 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/15120 (pow.f64 x 5)))))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(*.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 (exp.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2)))) 1)
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 -1 (neg.f64 (tan.f64 (.f64 x 1/2))))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (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 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2) -1) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2) -1))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2)) -1) (pow.f64 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) -1))
(/.f64 1 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1))
(/.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(/.f64 -1 (neg.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(/.f64 (tan.f64 (*.f64 x 1/2)) 1)
(/.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2))
(/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(/.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) -1)
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2))) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(/.f64 (neg.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))))
(log.f64 (+.f64 1 (expm1.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))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) 1))
(tan.f64 (*.f64 x 1/2))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))))) 1)
(.f64 1 (/.f64 1 (tan.f64 (.f64 x 1/2))))
(.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 1)
(.f64 -1 (/.f64 1 (neg.f64 (tan.f64 (.f64 x 1/2)))))
(.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2) (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2))
(.f64 (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) (cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -2)))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2)) (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (/.f64 1 (sin.f64 (.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(.f64 (pow.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) -1) (pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) -1))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) -1) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) -1))
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(pow.f64 (tan.f64 (*.f64 x 1/2)) -1)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2) 2)
(pow.f64 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3)
(pow.f64 (pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 3) 1/3)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -2))
(log.f64 (exp.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))))))
(cbrt.f64 (pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 3))
(expm1.f64 (log1p.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(exp.f64 (neg.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(exp.f64 (.f64 (neg.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) 1))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) -1))
(log1p.f64 (expm1.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(-.f64 (exp.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2)))) 1)
(.f64 1 (tan.f64 (.f64 x 1/2)))
(.f64 -1 (neg.f64 (tan.f64 (.f64 x 1/2))))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (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 (sin.f64 (.f64 x 1/2)) (/.f64 1 (cos.f64 (*.f64 x 1/2))))
(.f64 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2) -1) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2) -1))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2)) -1) (pow.f64 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) -1))
(/.f64 1 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
(/.f64 1 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1))
(/.f64 1 (/.f64 (cos.f64 (.f64 x 1/2)) (sin.f64 (.f64 x 1/2))))
(/.f64 -1 (neg.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(/.f64 (tan.f64 (*.f64 x 1/2)) 1)
(/.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2))
(/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(/.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) -1)
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))
(/.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2))) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(/.f64 (neg.f64 (sin.f64 (.f64 x 1/2))) (neg.f64 (cos.f64 (.f64 x 1/2))))
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -2) -1/2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(log.f64 (+.f64 1 (expm1.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))))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) 1))
(log1p.f64 (expm1.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 (.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 2 x)
(+.f64 (.f64 -1/6 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/6 x (/.f64 2 x))
(fma.f64 x -1/6 (/.f64 2 x))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/360 (pow.f64 x 3) (fma.f64 -1/6 x (/.f64 2 x)))
(fma.f64 (pow.f64 x 3) -1/360 (fma.f64 x -1/6 (/.f64 2 x)))
(fma.f64 x -1/6 (fma.f64 (pow.f64 x 3) -1/360 (/.f64 2 x)))
(+.f64 (.f64 -1/360 (pow.f64 x 3)) (+.f64 (.f64 -1/6 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/15120 (pow.f64 x 5)))))
(fma.f64 -1/360 (pow.f64 x 3) (+.f64 (fma.f64 -1/6 x (/.f64 2 x)) (*.f64 (pow.f64 x 5) -1/15120)))
(fma.f64 (pow.f64 x 3) -1/360 (fma.f64 x -1/6 (fma.f64 (pow.f64 x 5) -1/15120 (/.f64 2 x))))
(fma.f64 x -1/6 (fma.f64 (pow.f64 x 3) -1/360 (fma.f64 (pow.f64 x 5) -1/15120 (/.f64 2 x))))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(*.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))))
(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 (exp.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2)))) 1)
(tan.f64 (*.f64 1/2 x))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(.f64 -1 (neg.f64 (tan.f64 (.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(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))
(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))))
(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 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2) -1) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2) -1))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2)) -1) (pow.f64 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) -1))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2))) (/.f64 1 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)))
(/.f64 1 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(/.f64 1 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1))
(tan.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 -1 (neg.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(tan.f64 (*.f64 1/2 x))
(/.f64 (tan.f64 (*.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(/.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2))
(/.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (tan.f64 (.f64 1/2 x)) -1/2))
(/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(tan.f64 (*.f64 1/2 x))
(/.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) -1)
(tan.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 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2))) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2))) (/.f64 1 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)))
(/.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)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(log.f64 (+.f64 1 (expm1.f64 (tan.f64 (*.f64 x 1/2)))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) 1))
(tan.f64 (*.f64 1/2 x))
(tan.f64 (*.f64 x 1/2))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(-.f64 (exp.f64 (log1p.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))))) 1)
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(.f64 1 (/.f64 1 (tan.f64 (.f64 x 1/2))))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(.f64 (/.f64 1 (tan.f64 (.f64 x 1/2))) 1)
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(.f64 -1 (/.f64 1 (neg.f64 (tan.f64 (.f64 x 1/2)))))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2) (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(.f64 (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))) (cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -2)))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)) (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(/.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)) (cbrt.f64 (tan.f64 (.f64 1/2 x))))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2)) (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))))
(.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)) (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 1/2 x)))))
(/.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)) (cbrt.f64 (tan.f64 (.f64 1/2 x))))
(.f64 (/.f64 1 (sin.f64 (.f64 x 1/2))) (cos.f64 (*.f64 x 1/2)))
(/.f64 (cos.f64 (.f64 1/2 x)) (sin.f64 (.f64 1/2 x)))
(.f64 (pow.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) -1) (pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) -1))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) -1) (pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) -1))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1)
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(pow.f64 (tan.f64 (*.f64 x 1/2)) -1)
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2) 2)
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(pow.f64 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) 3)
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(pow.f64 (pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 3) 1/3)
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -2))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(log.f64 (exp.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))))))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(cbrt.f64 (pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 3))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(expm1.f64 (log1p.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(exp.f64 (neg.f64 (log.f64 (tan.f64 (*.f64 x 1/2)))))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(exp.f64 (.f64 (neg.f64 (log.f64 (tan.f64 (.f64 x 1/2)))) 1))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) -1))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(log1p.f64 (expm1.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(/.f64 1 (tan.f64 (*.f64 1/2 x)))
(-.f64 (exp.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2)))) 1)
(tan.f64 (*.f64 1/2 x))
(.f64 1 (tan.f64 (.f64 x 1/2)))
(tan.f64 (*.f64 1/2 x))
(.f64 -1 (neg.f64 (tan.f64 (.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(.f64 (tan.f64 (.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (sqrt.f64 (tan.f64 (*.f64 x 1/2))))
(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))
(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))))
(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 (pow.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2) -1) (pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -1/2) -1))
(tan.f64 (*.f64 1/2 x))
(.f64 (pow.f64 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2)) -1) (pow.f64 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 x 1/2)))) -1))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2))) (/.f64 1 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)))
(/.f64 1 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(/.f64 1 (/.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) 1))
(tan.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 -1 (neg.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2)))))
(tan.f64 (*.f64 1/2 x))
(/.f64 (tan.f64 (*.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(/.f64 (sqrt.f64 (tan.f64 (.f64 x 1/2))) (pow.f64 (tan.f64 (.f64 x 1/2)) -1/2))
(/.f64 (sqrt.f64 (tan.f64 (.f64 1/2 x))) (pow.f64 (tan.f64 (.f64 1/2 x)) -1/2))
(/.f64 (pow.f64 (cbrt.f64 (tan.f64 (.f64 x 1/2))) 2) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(tan.f64 (*.f64 1/2 x))
(/.f64 (neg.f64 (tan.f64 (*.f64 x 1/2))) -1)
(tan.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 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 x 1/2)) -2))) (/.f64 1 (cbrt.f64 (tan.f64 (.f64 x 1/2)))))
(.f64 (/.f64 1 (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2))) (/.f64 1 (/.f64 1 (cbrt.f64 (tan.f64 (*.f64 1/2 x))))))
(/.f64 (cbrt.f64 (tan.f64 (.f64 1/2 x))) (cbrt.f64 (pow.f64 (tan.f64 (.f64 1/2 x)) -2)))
(/.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 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (tan.f64 (*.f64 x 1/2)) 1)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (sqrt.f64 (tan.f64 (*.f64 x 1/2))) 2)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (cbrt.f64 (tan.f64 (*.f64 x 1/2))) 3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3) 1/3)
(tan.f64 (*.f64 1/2 x))
(pow.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) -2) -1/2)
(pow.f64 (pow.f64 (tan.f64 (*.f64 1/2 x)) -2) -1/2)
(sqrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 2))
(tan.f64 (*.f64 1/2 x))
(log.f64 (exp.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(log.f64 (+.f64 1 (expm1.f64 (tan.f64 (*.f64 x 1/2)))))
(tan.f64 (*.f64 1/2 x))
(cbrt.f64 (pow.f64 (tan.f64 (*.f64 x 1/2)) 3))
(tan.f64 (*.f64 1/2 x))
(expm1.f64 (log1p.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (log.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))
(exp.f64 (.f64 (log.f64 (tan.f64 (.f64 x 1/2))) 1))
(tan.f64 (*.f64 1/2 x))
(log1p.f64 (expm1.f64 (tan.f64 (*.f64 x 1/2))))
(tan.f64 (*.f64 1/2 x))

eval30.0ms (0.4%)

Compiler: Compiled 1080 to 915 computations (15.3% saved)

prune12.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	93	4	97

Error

Counts

97 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	29.9b	(pow.f64 (/.f64 2 x) -1)
▶	0.1b	(/.f64 1 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
✓	29.8b	(*.f64 1/2 x)
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 25 to 20 computations (20% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite75.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

1648×	`add-sqr-sqrt`
1626×	`*-un-lft-identity`
1512×	`add-cube-cbrt`
1498×	`add-cbrt-cube`
174×	`pow1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	11
1	206	11
2	2132	11

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

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

Outputs

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

simplify53.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1006×	`associate-r`
956×	`distribute-lft-in`
900×	`distribute-rgt-in`
836×	`*-commutative`
788×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	667
1	192	667
2	665	661
3	3284	661

Stop Event

1×	node limit

Counts

37 → 43

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

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 2 x) -1)

Compiler

Compiled 12 to 9 computations (25% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(pow.f64 (/.f64 2 x) -1)
0.0ms	x	@	-inf	(pow.f64 (/.f64 2 x) -1)
0.0ms	x	@	inf	(pow.f64 (/.f64 2 x) -1)

rewrite55.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

1316×	`add-sqr-sqrt`
1288×	`*-un-lft-identity`
1208×	`add-cube-cbrt`
1198×	`add-cbrt-cube`
1186×	`add-exp-log`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	151	7
2	1705	7

Stop Event

1×	node limit

Counts

1 → 28

Calls

Call 1

Inputs
(pow.f64 (/.f64 2 x) -1)

Outputs

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

simplify40.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1592×	`associate-/r*`
1126×	`associate-/l/`
870×	`unswap-sqr`
634×	`associate-/r/`
616×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	352
1	140	352
2	370	352
3	1664	352

Stop Event

1×	node limit

Counts

40 → 31

Calls

Call 1

Inputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(-.f64 (+.f64 1 (*.f64 x 1/2)) 1)
(*.f64 x 1/2)
(.f64 (.f64 x 1/2) 1)
(.f64 1 (.f64 x 1/2))
(.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)))
(.f64 (cbrt.f64 (.f64 x 1/2)) (cbrt.f64 (pow.f64 (/.f64 2 x) -2)))
(.f64 (cbrt.f64 (pow.f64 (/.f64 2 x) -2)) (cbrt.f64 (.f64 x 1/2)))
(*.f64 -1/2 (neg.f64 x))
(*.f64 1/2 x)
(*.f64 1/2 (pow.f64 (/.f64 1 x) -1))
(*.f64 (pow.f64 (sqrt.f64 (/.f64 2 x)) -1) (pow.f64 (sqrt.f64 (/.f64 2 x)) -1))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 2 x)) -1))
(/.f64 x 2)
(/.f64 -1 (neg.f64 (/.f64 2 x)))
(/.f64 1 (/.f64 2 x))
(/.f64 1 (/.f64 (/.f64 2 x) 1))
(/.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 2 x)))
(/.f64 (sqrt.f64 x) (/.f64 2 (sqrt.f64 x)))
(/.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 2 (cbrt.f64 x)))
(/.f64 (neg.f64 x) -2)
(/.f64 1/2 (/.f64 1 x))
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2)) (cbrt.f64 (/.f64 2 x)))
(sqrt.f64 (pow.f64 (/.f64 2 x) -2))
(log.f64 (exp.f64 (*.f64 x 1/2)))
(cbrt.f64 (pow.f64 (*.f64 x 1/2) 3))
(expm1.f64 (log1p.f64 (*.f64 x 1/2)))
(exp.f64 (log.f64 (*.f64 x 1/2)))
(log1p.f64 (expm1.f64 (*.f64 x 1/2)))

Outputs
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 x)
(-.f64 (+.f64 1 (*.f64 x 1/2)) 1)
(*.f64 1/2 x)
(*.f64 x 1/2)
(*.f64 1/2 x)
(.f64 (.f64 x 1/2) 1)
(*.f64 1/2 x)
(.f64 1 (.f64 x 1/2))
(*.f64 1/2 x)
(.f64 (sqrt.f64 (.f64 x 1/2)) (sqrt.f64 (*.f64 x 1/2)))
(*.f64 1/2 x)
(.f64 (cbrt.f64 (.f64 x 1/2)) (cbrt.f64 (pow.f64 (/.f64 2 x) -2)))
(.f64 (cbrt.f64 (.f64 1/2 x)) (cbrt.f64 (pow.f64 (/.f64 2 x) -2)))
(.f64 (cbrt.f64 (.f64 1/2 x)) (cbrt.f64 (.f64 1/4 (.f64 x x))))
(.f64 (cbrt.f64 (pow.f64 (/.f64 2 x) -2)) (cbrt.f64 (.f64 x 1/2)))
(.f64 (cbrt.f64 (.f64 1/2 x)) (cbrt.f64 (pow.f64 (/.f64 2 x) -2)))
(.f64 (cbrt.f64 (.f64 1/2 x)) (cbrt.f64 (.f64 1/4 (.f64 x x))))
(*.f64 -1/2 (neg.f64 x))
(*.f64 1/2 x)
(*.f64 1/2 x)
(*.f64 1/2 (pow.f64 (/.f64 1 x) -1))
(*.f64 1/2 x)
(*.f64 (pow.f64 (sqrt.f64 (/.f64 2 x)) -1) (pow.f64 (sqrt.f64 (/.f64 2 x)) -1))
(*.f64 1/2 x)
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2) -1) (pow.f64 (cbrt.f64 (/.f64 2 x)) -1))
(*.f64 1/2 x)
(/.f64 x 2)
(*.f64 1/2 x)
(/.f64 -1 (neg.f64 (/.f64 2 x)))
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(*.f64 1/2 x)
(/.f64 1 (/.f64 (/.f64 2 x) 1))
(*.f64 1/2 x)
(/.f64 (sqrt.f64 (*.f64 x 1/2)) (sqrt.f64 (/.f64 2 x)))
(/.f64 (sqrt.f64 (*.f64 1/2 x)) (sqrt.f64 (/.f64 2 x)))
(/.f64 (sqrt.f64 x) (/.f64 2 (sqrt.f64 x)))
(*.f64 1/2 x)
(/.f64 (pow.f64 (cbrt.f64 x) 2) (/.f64 2 (cbrt.f64 x)))
(*.f64 1/2 x)
(/.f64 (neg.f64 x) -2)
(*.f64 1/2 x)
(/.f64 1/2 (/.f64 1 x))
(*.f64 1/2 x)
(/.f64 (/.f64 1 (pow.f64 (cbrt.f64 (/.f64 2 x)) 2)) (cbrt.f64 (/.f64 2 x)))
(*.f64 1/2 x)
(sqrt.f64 (pow.f64 (/.f64 2 x) -2))
(*.f64 1/2 x)
(log.f64 (exp.f64 (*.f64 x 1/2)))
(*.f64 1/2 x)
(cbrt.f64 (pow.f64 (*.f64 x 1/2) 3))
(*.f64 1/2 x)
(expm1.f64 (log1p.f64 (*.f64 x 1/2)))
(*.f64 1/2 x)
(exp.f64 (log.f64 (*.f64 x 1/2)))
(*.f64 1/2 x)
(log1p.f64 (expm1.f64 (*.f64 x 1/2)))
(*.f64 1/2 x)

eval44.0ms (0.6%)

Compiler: Compiled 1261 to 1056 computations (16.3% saved)

prune16.0ms (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	120	5	125

Error

Counts

125 → 5

Alt Table

Click to see full alt table

Status	Error	Program
	29.9b	(/.f64 1 (/.f64 2 x))
✓	0.1b	(/.f64 1 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
	29.8b	(/.f64 1 (+.f64 (.f64 -1/6 x) (.f64 2 (/.f64 1 x))))
✓	29.8b	(*.f64 1/2 x)
✓	0.0b	(tan.f64 (/.f64 x 2))

Compiler

Compiled 36 to 30 computations (16.7% saved)

regimes12.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(/.f64 1 (+.f64 (.f64 -1/6 x) (.f64 2 (/.f64 1 x))))
(tan.f64 (/.f64 x 2))
(pow.f64 (/.f64 2 x) -1)
(/.f64 1 (/.f64 1 (tan.f64 (*.f64 x 1/2))))
(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))
(pow.f64 (/.f64 1 (tan.f64 (*.f64 x 1/2))) -1)
(/.f64 (sin.f64 (.f64 x 1/2)) (cos.f64 (.f64 x 1/2)))

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

Calls

2 calls:

5.0ms	x
4.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (sin.f64 x))

Results

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

Compiler

Compiled 71 to 56 computations (21.1% saved)

regimes5.0ms (0.1%)

Accuracy

Total -0.6b remaining (-2.1%)

Threshold costs -0.6b (-2.1%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 1/2 x)
(/.f64 1 (/.f64 2 x))
(/.f64 1 (+.f64 (.f64 -1/6 x) (.f64 2 (/.f64 1 x))))

Outputs
(*.f64 1/2 x)

Calls

1 calls:

4.0ms

Results

Error	Segments	Branch
29.8b	1	`x`

Compiler

Compiled 22 to 17 computations (22.7% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	10	18

Stop Event

1×	fuel
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)

soundness41.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

196×	`fma-def`
118×	`associate-r`
90×	`*-commutative`
80×	`associate-+l-`
74×	`associate-/l*`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11

Stop Event

1×

saturated

Compiler

Compiled 12 to 9 computations (25% saved)

end21.0ms (0.3%)

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

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11
0	1	1

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11
0	1	1

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11

Details

analyze282.0ms (3.6%)

sample6.4s (81.7%)

preprocess51.0ms (0.7%)

simplify26.0ms (0.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series1.0ms (0%)

rewrite77.0ms (1%)

simplify70.0ms (0.9%)

eval37.0ms (0.5%)

prune5.0ms (0.1%)

localize3.0ms (0%)

localize48.0ms (0.6%)

series0.0ms (0%)

rewrite88.0ms (1.1%)

simplify50.0ms (0.6%)

eval52.0ms (0.7%)

prune6.0ms (0.1%)

localize15.0ms (0.2%)

series3.0ms (0%)

rewrite63.0ms (0.8%)

simplify112.0ms (1.4%)

eval30.0ms (0.4%)

prune12.0ms (0.2%)

localize12.0ms (0.2%)

series0.0ms (0%)

rewrite75.0ms (1%)

simplify53.0ms (0.7%)

localize5.0ms (0.1%)

series2.0ms (0%)

rewrite55.0ms (0.7%)

simplify40.0ms (0.5%)

eval44.0ms (0.6%)

prune16.0ms (0.2%)

regimes12.0ms (0.2%)

regimes5.0ms (0.1%)

simplify4.0ms (0%)

soundness41.0ms (0.5%)

end21.0ms (0.3%)

Profiling

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11
0	1	1

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11

Iter	Nodes	Cost
0	9	11
1	19	11
2	25	11
3	36	11
4	58	11
5	85	11
6	126	11
7	206	11
8	368	11
9	598	11
10	817	11
11	861	11