Details

analyze729.0ms (8.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample1.7s (20.2%)

Results

758.0ms	2082×	body	1024	valid
483.0ms	4579×	body	128	valid
283.0ms	1036×	body	512	valid
115.0ms	552×	body	256	valid
3.0ms	7×	body	2048	valid

Compiler

Compiled 34 to 18 computations (47.1% saved)

preprocess32.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

627×	`times-frac_binary64`
563×	`div-sub_binary64`
543×	`fma-def_binary64`
333×	`fma-neg_binary64`
263×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	19	22
2	31	22
3	49	22
4	99	22
5	169	22
6	279	22
7	588	22
8	1466	22
9	3717	22
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 16 to 8 computations (50% saved)

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

627×	`times-frac_binary64`
563×	`div-sub_binary64`
543×	`fma-def_binary64`
333×	`fma-neg_binary64`
263×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	19	22
2	31	22
3	49	22
4	99	22
5	169	22
6	279	22
7	588	22
8	1466	22
9	3717	22

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (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
▶	0.4b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
	0.4b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (fma.f64 (tan.f64 x) (tan.f64 x) 1))

Compiler

Compiled 92 to 45 computations (51.1% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
✓	0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
✓	0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
✓	0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

series89.0ms (1.1%)

Counts

4 → 48

Calls

12 calls:

30.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))	x	-inf
28.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))	x	inf
5.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))	x	-inf
5.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))	x	inf
4.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))	x	-inf

rewrite88.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

434×	`log-prod_binary64`
381×	`prod-diff_binary64`
196×	`fma-def_binary64`
157×	`expm1-udef_binary64`
156×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	44
1	180	44
2	2544	44

Stop Event

1×	node limit

Counts

4 → 236

simplify35.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-def_binary64`
515×	`associate-l_binary64`
460×	`associate-r_binary64`
342×	`cancel-sign-sub-inv_binary64`
184×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	46	868
1	132	864
2	345	858
3	1101	856

Stop Event

1×	node limit

Counts

284 → 269

prune578.0ms (7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	294	14	308
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	296	14	310

Error

0.0b

Counts

310 → 14

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
	0.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.6b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 1 (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x))))))
	0.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) 4) 1) (fma.f64 (tan.f64 x) (tan.f64 x) -1)))
	0.9b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.6b	(/.f64 (fma.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (neg.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2))) 1) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 6))) (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1) (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1))))
	0.5b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
	0.7b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (hypot.f64 1 (tan.f64 x)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	1.2b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.5b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))

Compiler

Compiled 11739 to 6996 computations (40.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
✓	0.2b	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))
✓	0.2b	(*.f64 (sin.f64 x) (tan.f64 x))
	0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

series88.0ms (1.1%)

Counts

3 → 36

Calls

9 calls:

31.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))	x	inf
31.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))	x	-inf
8.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))	x	inf
7.0ms	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))	x	-inf
4.0ms	(*.f64 (sin.f64 x) (tan.f64 x))	x	-inf

rewrite63.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

282×	`fma-def_binary64`
217×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
184×	`fma-neg_binary64`
138×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	51
1	265	37
2	4056	37

Stop Event

1×	node limit

Counts

3 → 103

simplify27.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

660×	`fma-def_binary64`
628×	`associate-l_binary64`
543×	`associate-r_binary64`
342×	`cancel-sign-sub-inv_binary64`
184×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	665
1	136	665
2	351	661
3	1147	659

Stop Event

1×	node limit

Counts

139 → 127

prune264.0ms (3.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	164	2	166
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	166	14	180

Error

0.0b

Counts

180 → 14

Alt Table

Status	Error	Program
	0.6b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6)))))) (fma.f64 (neg.f64 (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))) (.f64 (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 6))))))
	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 1 (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x))))))
	0.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) 4) 1) (fma.f64 (tan.f64 x) (tan.f64 x) -1)))
	0.9b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.6b	(/.f64 (fma.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (neg.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2))) 1) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	1.2b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.7b	(/.f64 (fma.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (neg.f64 (pow.f64 (cbrt.f64 (tan.f64 x)) 2)) 1) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
▶	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 6))) (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1) (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1))))
	0.5b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
	0.5b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.7b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (hypot.f64 1 (tan.f64 x)))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (hypot.f64 1 (tan.f64 x))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (hypot.f64 1 (tan.f64 x))))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	0.5b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))

Compiler

Compiled 5012 to 2937 computations (41.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
✓	0.2b	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
✓	0.2b	(pow.f64 (sin.f64 x) 2)
✓	0.3b	(pow.f64 (cos.f64 x) 2)

series108.0ms (1.3%)

Counts

4 → 16

Calls

12 calls:

40.0ms	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))	x	inf
39.0ms	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))	x	-inf
9.0ms	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))	x	-inf
9.0ms	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))	x	inf
3.0ms	(pow.f64 (cos.f64 x) 2)	x	0

rewrite122.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

661×	`prod-diff_binary64`
218×	`log1p-udef_binary64`
130×	`add-sqr-sqrt_binary64`
128×	`pow1_binary64`
126×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	65
1	265	56
2	3517	56

Stop Event

1×	node limit

Counts

4 → 197

simplify33.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

645×	`cancel-sign-sub-inv_binary64`
425×	`sub-neg_binary64`
349×	`fma-neg_binary64`
178×	`unswap-sqr_binary64`
177×	`*-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	202
1	128	198
2	385	192
3	1344	192
4	4249	192

Stop Event

1×	node limit

Counts

213 → 222

prune917.0ms (11.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	275	2	277
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	278	13	291

Error

0.0b

Counts

291 → 13

Alt Table

Status	Error	Program
	0.9b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (sqrt.f64 (/.f64 1 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2))))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2))) (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2))))))
	0.9b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) 4) 1) (fma.f64 (tan.f64 x) (tan.f64 x) -1)))
	0.6b	(/.f64 (fma.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (neg.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2))) 1) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
✓	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 6))) (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1) (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1))))
	0.5b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
▶	0.5b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.5b	(/.f64 (/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 4) (pow.f64 (cos.f64 x) 4))) (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 1 (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x))))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	1.2b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.5b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))

Compiler

Compiled 16923 to 9482 computations (44% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x)))
	0.2b	(*.f64 (sin.f64 x) (tan.f64 x))
	0.2b	(pow.f64 (sin.f64 x) 2)
	0.3b	(pow.f64 (cos.f64 x) 2)

prune355.0ms (4.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	132	13	145

Error

0.0b

Counts

145 → 13

Alt Table

Status	Error	Program
	0.9b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (sqrt.f64 (/.f64 1 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2)))))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2))))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2))) (.f64 (/.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)))) (/.f64 (pow.f64 (cbrt.f64 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2) (cbrt.f64 (pow.f64 (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2)) 2))))))
	0.9b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 1 (pow.f64 (cbrt.f64 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) 2)))))
	0.5b	(/.f64 (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))) (/.f64 (-.f64 (pow.f64 (tan.f64 x) 4) 1) (fma.f64 (tan.f64 x) (tan.f64 x) -1)))
	0.6b	(/.f64 (fma.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (neg.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2))) 1) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
✓	0.4b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.6b	(+.f64 (fma.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 6))) (-.f64 (+.f64 1 (pow.f64 (tan.f64 x) 4)) (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1)))) (fma.f64 (neg.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1) (.f64 (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 2)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (/.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) 1))))
	0.5b	(+.f64 (fma.f64 (/.f64 1 (-.f64 1 (pow.f64 (tan.f64 x) 4))) (-.f64 1 (pow.f64 (tan.f64 x) 2)) (neg.f64 (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4)))))) (fma.f64 (neg.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))) (.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (/.f64 (pow.f64 (tan.f64 x) 2) (-.f64 1 (pow.f64 (tan.f64 x) 4))))))
✓	0.5b	(/.f64 (-.f64 1 (/.f64 (*.f64 (sin.f64 x) (tan.f64 x)) (cos.f64 x))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.5b	(/.f64 (/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 4) (pow.f64 (cos.f64 x) 4))) (+.f64 1 (pow.f64 (/.f64 (sin.f64 x) (cos.f64 x)) 2))) (+.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))))
	0.5b	(+.f64 (fma.f64 1 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (neg.f64 (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x)))))) (fma.f64 (neg.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x)))) (/.f64 1 (hypot.f64 1 (tan.f64 x))) (.f64 (/.f64 (pow.f64 (tan.f64 x) 2) (hypot.f64 1 (tan.f64 x))) (/.f64 1 (hypot.f64 1 (tan.f64 x))))))
	0.5b	(+.f64 (fma.f64 (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (sqrt.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (neg.f64 (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2)))) (fma.f64 (neg.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1))) (pow.f64 (tan.f64 x) 2) (.f64 (/.f64 1 (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (pow.f64 (tan.f64 x) 2))))
	1.2b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))) (log.f64 (sqrt.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
	0.5b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (fma.f64 (tan.f64 x) (tan.f64 x) 1)) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))

Compiler

Compiled 4158 to 2468 computations (40.6% saved)

regimes2.6s (31.2%)

Accuracy

Total 0.3b remaining (81.2%)

Threshold costs 0.3b (81.2%)

Counts

425 → 1

Compiler

Compiled 53800 to 36573 computations (32% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
5×	`*-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	34
1	17	34
2	23	34
3	33	34
4	40	34
5	45	34
6	47	34

Stop Event

1×

saturated

end388.0ms (4.7%)

Stop Event

1×

fuel

Compiler

Compiled 749 to 476 computations (36.4% saved)

Details

analyze729.0ms (8.9%)

sample1.7s (20.2%)

preprocess32.0ms (0.4%)

simplify25.0ms (0.3%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series89.0ms (1.1%)

rewrite88.0ms (1.1%)

simplify35.0ms (0.4%)

prune578.0ms (7%)

localize11.0ms (0.1%)

series88.0ms (1.1%)

rewrite63.0ms (0.8%)

simplify27.0ms (0.3%)

prune264.0ms (3.2%)

localize10.0ms (0.1%)

series108.0ms (1.3%)

rewrite122.0ms (1.5%)

simplify33.0ms (0.4%)

prune917.0ms (11.2%)

localize14.0ms (0.2%)

prune355.0ms (4.3%)

regimes2.6s (31.2%)

simplify3.0ms (0%)

end388.0ms (4.7%)

Profiling