Details

analyze1.4s (4.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

Compiler

Compiled 53 to 41 computations (22.6% saved)

sample8.8s (30.6%)

Results

5.8s	3520×	body	1024	valid
1.5s	1487×	body	512	valid
940.0ms	2645×	body	128	valid
444.0ms	578×	body	256	valid
82.0ms	26×	body	2048	valid

Compiler

Compiled 106 to 82 computations (22.6% saved)

preprocess32.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

736×	`distribute-rgt-in_binary64`
734×	`distribute-lft-in_binary64`
515×	`fma-def_binary64`
127×	`distribute-lft-neg-out_binary64`
127×	`distribute-rgt-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	160
1	120	148
2	353	148
3	1524	146
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 52 to 40 computations (23.1% saved)

simplify26.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

444×	`distribute-rgt-neg-out_binary64`
418×	`distribute-rgt-in_binary64`
417×	`distribute-lft-in_binary64`
350×	`unsub-neg_binary64`
270×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	80	74
2	211	74
3	809	73
4	3815	73

Stop Event

1×	node limit

Counts

1 → 2

prune7.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))

Status

Error

Program

▶

0.5b

(/.f64 (+.f64 2 (*.f64 (*.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (*.f64 3 (+.f64 (+.f64 1 (*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))

0.5b

(/.f64 (fma.f64 (sqrt.f64 2) (*.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))

Compiler

Compiled 298 to 221 computations (25.8% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
✓	0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
✓	1.0b	(-.f64 3 (sqrt.f64 5))
✓	3.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series567.0ms (2%)

Counts

4 → 56

Calls

18 calls:

137.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))	y	inf
118.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))	y	-inf
112.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))	x	inf
99.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))	x	-inf
40.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))	y	0

rewrite51.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

383×	`log1p-expm1-u_binary64`
383×	`expm1-log1p-u_binary64`
369×	`add-log-exp_binary64`
368×	`add-exp-log_binary64`
348×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	110
1	794	104

Stop Event

1×	node limit

Counts

4 → 74

simplify140.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-r_binary64`
369×	`fma-def_binary64`
290×	`associate-+r+_binary64`
239×	`+-commutative_binary64`
234×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	353	7149
1	1210	6942
2	4990	6942

Stop Event

1×	node limit

Counts

130 → 124

prune422.0ms (1.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Error

0.0b

Counts

126 → 13

Alt Table

Status	Error	Program
▶	0.5b	(pow.f64 (/.f64 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2)) -1)
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
	0.7b	(.f64 1/3 (/.f64 (-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (cos.f64 y) (sqrt.f64 2)))) (+.f64 2 (+.f64 (.f64 1/16 (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)))) (.f64 257/256 (.f64 (sin.f64 y) (.f64 (sqrt.f64 2) (.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (sqrt.f64 2) (cos.f64 x)))) (+.f64 (.f64 257/256 (.f64 (sin.f64 y) (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (sin.f64 x))))) (.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))))) (-.f64 (+.f64 1 (+.f64 (.f64 3/2 (cos.f64 y)) (.f64 1/2 (.f64 (cos.f64 x) (sqrt.f64 5))))) (+.f64 (.f64 1/2 (.f64 (cos.f64 y) (sqrt.f64 5))) (*.f64 1/2 (cos.f64 x))))))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 2)
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (/.f64 1 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))
	0.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))))
	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))) 1)
	0.6b	(log.f64 (exp.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))))
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 3)
	0.5b	(pow.f64 (pow.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))) 3) 1/3)
	0.5b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)))))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
	0.6b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5)))) 2) (cos.f64 y)))))

Compiler

Compiled 12750 to 9167 computations (28.1% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))
✓	0.4b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))))
✓	1.0b	(-.f64 3/2 (/.f64 (sqrt.f64 5) 2))
	3.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series45.0ms (0.2%)

Counts

3 → 48

Calls

12 calls:

6.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))))	x	-inf
5.0ms	(.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))	x	-inf
5.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))))	x	inf
5.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))))	y	-inf
5.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))))	y	inf

rewrite45.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
203×	`add-cbrt-cube_binary64`
199×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	62
1	429	59

Stop Event

1×	node limit

Counts

3 → 67

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

595×	`distribute-rgt-neg-in_binary64`
522×	`fma-def_binary64`
380×	`associate-l_binary64`
343×	`associate-r_binary64`
247×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	1321
1	272	1257
2	919	1100
3	3876	1100

Stop Event

1×	node limit

Counts

115 → 101

prune511.0ms (1.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	144	13	157

Error

0.0b

Counts

157 → 13

Alt Table

Status	Error	Program
	0.5b	(pow.f64 (/.f64 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (pow.f64 (cbrt.f64 (-.f64 (cos.f64 x) (cos.f64 y))) 3) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2)) -1)
	0.5b	(pow.f64 (/.f64 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (cos.f64 x)) 2) (cbrt.f64 (cos.f64 x)) (neg.f64 (.f64 (cos.f64 y) 1))) (fma.f64 (neg.f64 (cos.f64 y)) 1 (.f64 (cos.f64 y) 1))) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2)) -1)
	0.6b	(log.f64 (exp.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))))
	0.7b	(.f64 1/3 (/.f64 (-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (cos.f64 y) (sqrt.f64 2)))) (+.f64 2 (+.f64 (.f64 1/16 (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)))) (.f64 257/256 (.f64 (sin.f64 y) (.f64 (sqrt.f64 2) (.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (sqrt.f64 2) (cos.f64 x)))) (+.f64 (.f64 257/256 (.f64 (sin.f64 y) (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (sin.f64 x))))) (.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))))) (-.f64 (+.f64 1 (+.f64 (.f64 3/2 (cos.f64 y)) (.f64 1/2 (.f64 (cos.f64 x) (sqrt.f64 5))))) (+.f64 (.f64 1/2 (.f64 (cos.f64 y) (sqrt.f64 5))) (*.f64 1/2 (cos.f64 x))))))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 2)
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (/.f64 1 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))
	0.5b	(expm1.f64 (log1p.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))))
	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))) 1)
	0.5b	(pow.f64 (/.f64 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (+.f64 (fma.f64 1 (cos.f64 x) (neg.f64 (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)))) (fma.f64 (neg.f64 (cbrt.f64 (cos.f64 y))) (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (cos.f64 y)) 2)))) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2)) -1)
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 3)
	0.6b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5)))) 2) (cos.f64 y)))))
▶	0.4b	(pow.f64 (/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2)) -1)

Compiler

Compiled 9544 to 6559 computations (31.3% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2))
	0.3b	(.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))
	0.4b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))))
	3.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series1.4s (4.8%)

Counts

1 → 24

Calls

6 calls:

274.0ms	(/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2))	y	0
235.0ms	(/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2))	x	0
225.0ms	(/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2))	y	inf
220.0ms	(/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2))	x	inf
214.0ms	(/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2))	y	-inf

rewrite37.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

361×	`log1p-expm1-u_binary64`
361×	`expm1-log1p-u_binary64`
358×	`add-cbrt-cube_binary64`
350×	`add-log-exp_binary64`
349×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	74
1	766	72

Stop Event

1×	node limit

Counts

1 → 17

simplify204.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

884×	`associate-/r*_binary64`
850×	`fma-def_binary64`
368×	`*-commutative_binary64`
218×	`+-commutative_binary64`
198×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	815	17155
1	3075	15831

Stop Event

1×	node limit

Counts

41 → 35

prune1.3s (4.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	151	2	153
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	155	11	166

Error

0.0b

Counts

166 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 1/3 (/.f64 (-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (cos.f64 y) (sqrt.f64 2)))) (+.f64 2 (+.f64 (.f64 1/16 (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)))) (.f64 257/256 (.f64 (sin.f64 y) (.f64 (sqrt.f64 2) (.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (sqrt.f64 2) (cos.f64 x)))) (+.f64 (.f64 257/256 (.f64 (sin.f64 y) (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (sin.f64 x))))) (.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))))) (-.f64 (+.f64 1 (+.f64 (.f64 3/2 (cos.f64 y)) (.f64 1/2 (.f64 (cos.f64 x) (sqrt.f64 5))))) (+.f64 (.f64 1/2 (.f64 (cos.f64 y) (sqrt.f64 5))) (*.f64 1/2 (cos.f64 x))))))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 2)
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (/.f64 1 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))
	0.6b	(log.f64 (exp.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))))
	0.6b	(pow.f64 (.f64 3 (/.f64 (+.f64 1 (+.f64 (fma.f64 1/2 (.f64 (cos.f64 x) (sqrt.f64 5)) (/.f64 (cos.f64 y) (+.f64 3/2 (sqrt.f64 5/4)))) (.f64 (cos.f64 x) -1/2))) (-.f64 (+.f64 (fma.f64 (.f64 1/16 (pow.f64 (sin.f64 y) 2)) (.f64 (sqrt.f64 2) (cos.f64 y)) 2) (fma.f64 1/16 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)) (cos.f64 y)) (.f64 257/256 (.f64 (.f64 (sin.f64 y) (sqrt.f64 2)) (.f64 (cos.f64 x) (sin.f64 x)))))) (fma.f64 1/16 (.f64 (.f64 (cos.f64 x) (sqrt.f64 2)) (pow.f64 (sin.f64 y) 2)) (fma.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (cos.f64 x) (pow.f64 (sin.f64 x) 2))) (.f64 257/256 (.f64 (.f64 (sin.f64 y) (cos.f64 y)) (*.f64 (sqrt.f64 2) (sin.f64 x))))))))) -1)
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 3)
▶	0.5b	(pow.f64 (pow.f64 (pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3) 1/3) -1)
	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))) 1)
	0.6b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5)))) 2) (cos.f64 y)))))
✓	0.4b	(pow.f64 (/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2)) -1)

Compiler

Compiled 27097 to 19786 computations (27% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))
✓	0.4b	(.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)))
✓	0.5b	(pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3)
	3.0b	(-.f64 (cos.f64 x) (cos.f64 y))

series7.3s (25.4%)

Counts

3 → 72

Calls

18 calls:

4.5s	(pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3)	y	0
1.7s	(pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3)	x	0
304.0ms	(pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3)	y	-inf
277.0ms	(pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3)	x	-inf
270.0ms	(pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3)	y	inf

rewrite50.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

364×	`log1p-expm1-u_binary64`
364×	`expm1-log1p-u_binary64`
360×	`add-cbrt-cube_binary64`
351×	`add-log-exp_binary64`
350×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	120
1	781	120

Stop Event

1×	node limit

Counts

3 → 42

simplify727.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-def_binary64`
393×	`times-frac_binary64`
38×	`sqr-pow_binary64`
25×	`sub-neg_binary64`
15×	`cube-mult_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3222	77657

Stop Event

1×	node limit

Counts

114 → 86

prune3.2s (11.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	129	11	140

Error

0.0b

Counts

140 → 11

Alt Table

Status	Error	Program
	0.7b	(.f64 1/3 (/.f64 (-.f64 (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (cos.f64 y) (sqrt.f64 2)))) (+.f64 2 (+.f64 (.f64 1/16 (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)))) (.f64 257/256 (.f64 (sin.f64 y) (.f64 (sqrt.f64 2) (.f64 (sin.f64 x) (cos.f64 x)))))))) (+.f64 (.f64 1/16 (.f64 (pow.f64 (sin.f64 y) 2) (.f64 (sqrt.f64 2) (cos.f64 x)))) (+.f64 (.f64 257/256 (.f64 (sin.f64 y) (.f64 (cos.f64 y) (.f64 (sqrt.f64 2) (sin.f64 x))))) (.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (pow.f64 (sin.f64 x) 2) (cos.f64 x))))))) (-.f64 (+.f64 1 (+.f64 (.f64 3/2 (cos.f64 y)) (.f64 1/2 (.f64 (cos.f64 x) (sqrt.f64 5))))) (+.f64 (.f64 1/2 (.f64 (cos.f64 y) (sqrt.f64 5))) (*.f64 1/2 (cos.f64 x))))))
	0.6b	(pow.f64 (sqrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 2)
	0.5b	(/.f64 (fma.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))) 2) (+.f64 (/.f64 (*.f64 (cos.f64 x) (+.f64 (sqrt.f64 5) -1)) 2/3) (fma.f64 (cos.f64 y) (-.f64 9/2 (/.f64 (sqrt.f64 5) 2/3)) 3)))
	0.5b	(.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (/.f64 1 (.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))
	0.6b	(log.f64 (exp.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))))
	0.6b	(pow.f64 (.f64 3 (/.f64 (+.f64 1 (+.f64 (fma.f64 1/2 (.f64 (cos.f64 x) (sqrt.f64 5)) (/.f64 (cos.f64 y) (+.f64 3/2 (sqrt.f64 5/4)))) (.f64 (cos.f64 x) -1/2))) (-.f64 (+.f64 (fma.f64 (.f64 1/16 (pow.f64 (sin.f64 y) 2)) (.f64 (sqrt.f64 2) (cos.f64 y)) 2) (fma.f64 1/16 (.f64 (.f64 (sqrt.f64 2) (pow.f64 (sin.f64 x) 2)) (cos.f64 y)) (.f64 257/256 (.f64 (.f64 (sin.f64 y) (sqrt.f64 2)) (.f64 (cos.f64 x) (sin.f64 x)))))) (fma.f64 1/16 (.f64 (.f64 (cos.f64 x) (sqrt.f64 2)) (pow.f64 (sin.f64 y) 2)) (fma.f64 1/16 (.f64 (sqrt.f64 2) (.f64 (cos.f64 x) (pow.f64 (sin.f64 x) 2))) (.f64 257/256 (.f64 (.f64 (sin.f64 y) (cos.f64 y)) (*.f64 (sqrt.f64 2) (sin.f64 x))))))))) -1)
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))))) 3)
✓	0.5b	(pow.f64 (pow.f64 (pow.f64 (/.f64 3 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16))) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16))) 2) (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (fma.f64 (sqrt.f64 5) 1/2 -1/2) 1)))) 3) 1/3) -1)
	1.0b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (.f64 (sin.f64 x) 1/16)))) 2) (*.f64 3 (fma.f64 (cos.f64 y) (-.f64 3/2 (/.f64 (sqrt.f64 5) 2)) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1)))))) 1)
	0.6b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (log.f64 (exp.f64 (-.f64 3 (sqrt.f64 5)))) 2) (cos.f64 y)))))
✓	0.4b	(pow.f64 (/.f64 (.f64 3 (fma.f64 (cos.f64 y) (/.f64 1 (+.f64 3/2 (sqrt.f64 5/4))) (fma.f64 (cos.f64 x) (-.f64 (/.f64 (sqrt.f64 5) 2) 1/2) 1))) (fma.f64 (-.f64 (cos.f64 x) (cos.f64 y)) (.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 x) (.f64 (sin.f64 y) 1/16)) (-.f64 (sin.f64 y) (*.f64 (sin.f64 x) 1/16)))) 2)) -1)

Compiler

Compiled 102537 to 79367 computations (22.6% saved)

regimes1.8s (6.4%)

Accuracy

Total 0.4b remaining (90%)

Threshold costs 0.4b (90%)

Counts

203 → 1

Compiler

Compiled 39962 to 30586 computations (23.5% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
10×	`*-commutative_binary64`
9×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	77
1	59	77
2	79	77
3	89	77
4	96	77
5	98	77

Stop Event

1×

saturated

end476.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 786 to 592 computations (24.7% saved)

Details

analyze1.4s (4.8%)

sample8.8s (30.6%)

preprocess32.0ms (0.1%)

simplify26.0ms (0.1%)

prune7.0ms (0%)

localize33.0ms (0.1%)

series567.0ms (2%)

rewrite51.0ms (0.2%)

simplify140.0ms (0.5%)

prune422.0ms (1.5%)

localize30.0ms (0.1%)

series45.0ms (0.2%)

rewrite45.0ms (0.2%)

simplify51.0ms (0.2%)

prune511.0ms (1.8%)

localize34.0ms (0.1%)

series1.4s (4.8%)

rewrite37.0ms (0.1%)

simplify204.0ms (0.7%)

prune1.3s (4.6%)

localize40.0ms (0.1%)

series7.3s (25.4%)

rewrite50.0ms (0.2%)

simplify727.0ms (2.5%)

prune3.2s (11.2%)

regimes1.8s (6.4%)

simplify4.0ms (0%)

end476.0ms (1.7%)

Profiling