Details

analyze3.6s (10.9%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	99.9%	0.1%	9
0%	99.9%	0.1%	10
0%	99.5%	0.5%	11
0%	99.1%	0.9%	12
0.4%	97.3%	2.3%	13
0.7%	95.8%	3.5%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample18.1s (54.7%)

Results

5.2s	1281×	body	4096	invalid
4.0s	3964×	body	1024	valid
2.9s	1134×	body	2048	invalid
1.7s	1101×	body	2048	valid
1.3s	475×	body	4096	valid
1.0s	1429×	body	512	valid
657.0ms	694×	body	1024	invalid
354.0ms	526×	body	512	invalid
272.0ms	1086×	body	128	invalid
231.0ms	498×	body	256	valid
210.0ms	789×	body	128	valid
136.0ms	292×	body	256	invalid

Compiler

Compiled 86 to 65 computations (24.4% saved)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

300×	`rules-4_binary64`
288×	`rules-6_binary64`
272×	`rules-5-rev_binary64`
256×	`rules-4-rev_binary64`
238×	`rules-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	35
1	42	32
2	121	32
3	579	32
4	4999	32
5	4962	32

prune4.0ms (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

39.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	39.8b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))

Compiler

Compiled 97 to 65 computations (33% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
✓	1.2b	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
✓	13.3b	(/.f64 (pow.f64 t 3) (*.f64 l l))
✓	27.5b	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

series316.0ms (1%)

Counts

4 → 132

Calls

4 calls:

113.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))
106.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
64.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
31.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite134.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

499×	`prod-diff_binary64`
241×	`egg-rr`
153×	`add-sqr-sqrt_binary64`
145×	`log1p-expm1-u_binary64`
145×	`expm1-log1p-u_binary64`

Counts

4 → 241

Calls

4 calls:

127.0ms	(.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
127.0ms	(.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k))
127.0ms	(/.f64 (pow.f64 t 3) (*.f64 l l))
127.0ms	(.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	74
1	368	74
2	4305	74
3	5245	74
0	0	0
1	0	0

simplify103.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

673×	`fma-neg_binary64`
569×	`fma-def_binary64`
374×	`rules-20_binary64`
349×	`rules-13_binary64`
268×	`rules-6_binary64`

Counts

373 → 273

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	85	2796
1	241	2786
2	1120	2680
3	4826	2680
4	5412	2680

prune471.0ms (1.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	258	15	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	259	15	274

Error

14.3b

Counts

274 → 15

Alt Table

Status	Error	Program
	30.4b	(/.f64 2 (+.f64 (/.f64 (.f64 (pow.f64 k 4) t) (pow.f64 l 2)) (.f64 1/6 (/.f64 (*.f64 (pow.f64 k 6) t) (pow.f64 l 2)))))
	37.1b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 t (/.f64 (.f64 t t) (.f64 l l))) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	38.4b	(/.f64 2 (.f64 (.f64 (/.f64 (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) l)) l) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	56.7b	(/.f64 2 (pow.f64 (.f64 (/.f64 k t) (.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (sqrt.f64 (tan.f64 k)))) 2))
	55.6b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k t) (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (/.f64 k t)) (neg.f64 (.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k))))) (fma.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))))))
	47.1b	(/.f64 2 (.f64 (.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 t 3/2) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l)) (neg.f64 (.f64 0 (sin.f64 k)))) (fma.f64 0 (sin.f64 k) (*.f64 0 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	29.0b	(/.f64 2 (.f64 (+.f64 (fma.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) (.f64 (tan.f64 k) (pow.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 2)) (neg.f64 (.f64 0 (tan.f64 k)))) (fma.f64 0 (tan.f64 k) (.f64 0 (tan.f64 k)))) (pow.f64 (/.f64 k t) 2)))
	29.0b	(/.f64 2 (.f64 (.f64 (+.f64 (fma.f64 (pow.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) 2) (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (sin.f64 k)) (neg.f64 (.f64 0 (sin.f64 k)))) (fma.f64 0 (sin.f64 k) (*.f64 0 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	40.8b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k t) (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (/.f64 k t)) (neg.f64 (.f64 0 (pow.f64 (/.f64 k t) 2)))) (fma.f64 0 (pow.f64 (/.f64 k t) 2) (.f64 0 (pow.f64 (/.f64 k t) 2)))))
	30.7b	(/.f64 2 (fma.f64 t (/.f64 (pow.f64 k 4) (.f64 l l)) (.f64 (/.f64 t (.f64 l l)) (+.f64 (.f64 1/6 (pow.f64 k 6)) (*.f64 31/360 (pow.f64 k 8))))))
	29.2b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (pow.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) 2)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
▶	22.0b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	29.0b	(/.f64 2 (.f64 (.f64 (fma.f64 (pow.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 2) (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 0) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	47.2b	(/.f64 2 (.f64 (.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 t 3/2) l) 2) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	48.9b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (pow.f64 t 3/2) (/.f64 (pow.f64 t 3/2) (*.f64 l l))) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))

Compiler

Compiled 11514 to 6259 computations (45.6% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(pow.f64 (sin.f64 k) 2)
✓	1.6b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	6.2b	(.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))
✓	19.4b	(/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2)))

series222.0ms (0.7%)

Counts

4 → 16

Calls

4 calls:

126.0ms	(/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2)))
25.0ms	(.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))
13.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
6.0ms	(pow.f64 (sin.f64 k) 2)

rewrite111.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

491×	`prod-diff_binary64`
241×	`log1p-udef_binary64`
214×	`egg-rr`
138×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`

Counts

4 → 214

Calls

4 calls:

106.0ms	(pow.f64 (sin.f64 k) 2)
106.0ms	(*.f64 t (pow.f64 (sin.f64 k) 2))
106.0ms	(.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2)))
106.0ms	(/.f64 (.f64 (pow.f64 k 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (*.f64 (cos.f64 k) (pow.f64 l 2)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	329	50
2	3930	50
3	5303	50
0	0	0
1	0	0

simplify38.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

724×	`rules-4_binary64`
383×	`fma-def_binary64`
312×	`fma-neg_binary64`
272×	`rules-11_binary64`
258×	`rules-20_binary64`

Counts

230 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	410
1	201	382
2	972	346
3	5157	346

prune623.0ms (1.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	234	11	245
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	239	21	260

Error

7.7b

Counts

260 → 21

Alt Table

Status	Error	Program
	22.9b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (+.f64 (fma.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 4)) (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) t) (neg.f64 (.f64 0 t))) (fma.f64 0 t (.f64 0 t)))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	46.7b	(/.f64 2 (pow.f64 (/.f64 (.f64 k (.f64 (sin.f64 k) (sqrt.f64 t))) (*.f64 l (sqrt.f64 (cos.f64 k)))) 2))
	38.4b	(/.f64 2 (.f64 (.f64 (/.f64 (*.f64 (sin.f64 k) (/.f64 (pow.f64 t 3) l)) l) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	56.7b	(/.f64 2 (pow.f64 (.f64 (/.f64 k t) (.f64 (*.f64 (/.f64 (pow.f64 t 3/2) l) (sqrt.f64 (sin.f64 k))) (sqrt.f64 (tan.f64 k)))) 2))
	55.6b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k t) (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (/.f64 k t)) (neg.f64 (.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k))))) (fma.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))))))
	47.1b	(/.f64 2 (.f64 (.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 t 3/2) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l)) (neg.f64 (.f64 0 (sin.f64 k)))) (fma.f64 0 (sin.f64 k) (*.f64 0 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	22.4b	(/.f64 2 (.f64 (cbrt.f64 (.f64 t (/.f64 (pow.f64 (.f64 (sin.f64 k) k) 2) (.f64 (cos.f64 k) (.f64 l l))))) (pow.f64 (cbrt.f64 (.f64 t (/.f64 (pow.f64 (.f64 (sin.f64 k) k) 2) (.f64 (cos.f64 k) (*.f64 l l))))) 2)))
	29.0b	(/.f64 2 (.f64 (+.f64 (fma.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) (.f64 (tan.f64 k) (pow.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 2)) (neg.f64 (.f64 0 (tan.f64 k)))) (fma.f64 0 (tan.f64 k) (.f64 0 (tan.f64 k)))) (pow.f64 (/.f64 k t) 2)))
	29.0b	(/.f64 2 (.f64 (.f64 (+.f64 (fma.f64 (pow.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) 2) (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (sin.f64 k)) (neg.f64 (.f64 0 (sin.f64 k)))) (fma.f64 0 (sin.f64 k) (*.f64 0 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	40.8b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k t) (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (/.f64 k t)) (neg.f64 (.f64 0 (pow.f64 (/.f64 k t) 2)))) (fma.f64 0 (pow.f64 (/.f64 k t) 2) (.f64 0 (pow.f64 (/.f64 k t) 2)))))
	22.1b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (.f64 (cbrt.f64 (sin.f64 k)) (.f64 (sin.f64 k) (pow.f64 (cbrt.f64 (sin.f64 k)) 2))))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
▶	20.0b	(/.f64 2 (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l)))))
	29.0b	(/.f64 2 (.f64 (.f64 (fma.f64 (pow.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 2) (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 0) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	28.6b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (-.f64 (exp.f64 (log1p.f64 (pow.f64 (sin.f64 k) 2))) 1))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	47.2b	(/.f64 2 (.f64 (.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 t 3/2) l) 2) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	22.2b	(/.f64 2 (.f64 t (/.f64 (pow.f64 (.f64 (sin.f64 k) k) 2) (.f64 (cos.f64 k) (.f64 l l)))))
	40.9b	(/.f64 2 (/.f64 (pow.f64 (.f64 k (.f64 (sin.f64 k) (sqrt.f64 t))) 2) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	20.1b	(/.f64 2 (/.f64 (+.f64 (fma.f64 k (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) k) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (.f64 (cos.f64 k) (pow.f64 l 2))))
	22.1b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (+.f64 (fma.f64 (cbrt.f64 t) (.f64 (pow.f64 (sin.f64 k) 2) (pow.f64 (cbrt.f64 t) 2)) (neg.f64 (.f64 0 t))) (fma.f64 0 t (.f64 0 t)))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	22.0b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (/.f64 (sin.f64 k) (/.f64 1 (sin.f64 k))))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
	29.2b	(/.f64 2 (.f64 (.f64 (.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (pow.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) 2)) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))

Compiler

Compiled 8610 to 5210 computations (39.5% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(pow.f64 (sin.f64 k) 2)
	1.6b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	6.7b	(.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l))))
✓	15.4b	(/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l)))

series159.0ms (0.5%)

Counts

2 → 60

Calls

2 calls:

118.0ms	(.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l))))
42.0ms	(/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l)))

rewrite98.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

542×	`prod-diff_binary64`
140×	`add-sqr-sqrt_binary64`
132×	`log1p-expm1-u_binary64`
132×	`expm1-log1p-u_binary64`
130×	`add-cbrt-cube_binary64`

Counts

2 → 123

Calls

2 calls:

93.0ms	(.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l))))
93.0ms	(/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	331	38
2	4022	38
3	5076	38
0	0	0
1	0	0

simplify79.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

532×	`rules-21_binary64`
379×	`rules-10_binary64`
329×	`fma-def_binary64`
316×	`rules-10-rev_binary64`
247×	`rules-13_binary64`

Counts

183 → 143

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	1410
1	153	1398
2	625	1372
3	3190	1350
4	4833	1350
5	5014	1350

prune529.0ms (1.6%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	254	11	265
Fresh	13	7	20
Picked	0	1	1
Done	0	0	0
Total	267	19	286

Error

4.3b

Counts

286 → 19

Alt Table

Status	Error	Program
	18.3b	(/.f64 2 (/.f64 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) l) (.f64 (cos.f64 k) l)))
	46.5b	(/.f64 2 (+.f64 (fma.f64 (.f64 (sin.f64 k) (sqrt.f64 t)) (.f64 (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2) (.f64 (sin.f64 k) (sqrt.f64 t))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	55.6b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k t) (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (/.f64 k t)) (neg.f64 (.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k))))) (fma.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (.f64 0 (.f64 (.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))))))
	47.1b	(/.f64 2 (.f64 (.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 t 3/2) l) (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) l)) (neg.f64 (.f64 0 (sin.f64 k)))) (fma.f64 0 (sin.f64 k) (*.f64 0 (sin.f64 k)))) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	29.0b	(/.f64 2 (.f64 (+.f64 (fma.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) (.f64 (tan.f64 k) (pow.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 2)) (neg.f64 (.f64 0 (tan.f64 k)))) (fma.f64 0 (tan.f64 k) (.f64 0 (tan.f64 k)))) (pow.f64 (/.f64 k t) 2)))
	40.8b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k t) (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (/.f64 k t)) (neg.f64 (.f64 0 (pow.f64 (/.f64 k t) 2)))) (fma.f64 0 (pow.f64 (/.f64 k t) 2) (.f64 0 (pow.f64 (/.f64 k t) 2)))))
	22.1b	(/.f64 2 (/.f64 (.f64 (pow.f64 k 2) (.f64 t (.f64 (cbrt.f64 (sin.f64 k)) (.f64 (sin.f64 k) (pow.f64 (cbrt.f64 (sin.f64 k)) 2))))) (*.f64 (cos.f64 k) (pow.f64 l 2))))
✓	20.0b	(/.f64 2 (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l)))))
	34.5b	(/.f64 2 (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (pow.f64 (cbrt.f64 (pow.f64 (/.f64 k (*.f64 l (sqrt.f64 (cos.f64 k)))) 2)) 3)))
	47.2b	(/.f64 2 (.f64 (.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 t 3/2) l) 2) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	31.4b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k))))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	20.1b	(/.f64 2 (/.f64 (+.f64 (fma.f64 k (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) k) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (.f64 (cos.f64 k) (pow.f64 l 2))))
	45.7b	(/.f64 2 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) (*.f64 (sin.f64 k) (sqrt.f64 t))) 2)) 3))
	34.5b	(/.f64 2 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 t (pow.f64 (sin.f64 k) 2))) 2) (.f64 (cbrt.f64 (.f64 t (pow.f64 (sin.f64 k) 2))) (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2)) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
▶	17.0b	(/.f64 2 (+.f64 (fma.f64 k (.f64 (/.f64 k (.f64 (cos.f64 k) (.f64 l l))) (.f64 t (pow.f64 (sin.f64 k) 2))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	22.0b	(/.f64 2 (/.f64 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)) (.f64 l l)))
	20.1b	(/.f64 2 (.f64 (pow.f64 (cbrt.f64 (.f64 t (pow.f64 (sin.f64 k) 2))) 3) (/.f64 (.f64 k k) (.f64 (cos.f64 k) (*.f64 l l)))))
	34.4b	(/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 1 (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2))))
	34.4b	(/.f64 2 (+.f64 (fma.f64 t (.f64 (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2) (pow.f64 (sin.f64 k) 2)) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))

Compiler

Compiled 9812 to 4721 computations (51.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.6b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	3.6b	(fma.f64 k (.f64 (/.f64 k (.f64 (cos.f64 k) (.f64 l l))) (.f64 t (pow.f64 (sin.f64 k) 2))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)))))
✓	7.5b	(.f64 (/.f64 k (.f64 (cos.f64 k) (.f64 l l))) (.f64 t (pow.f64 (sin.f64 k) 2)))
✓	9.2b	(/.f64 k (.f64 (cos.f64 k) (.f64 l l)))

series273.0ms (0.8%)

Counts

3 → 96

Calls

3 calls:

127.0ms

(fma.f64 k (*.f64 (/.f64 k (*.f64 (cos.f64 k) (*.f64 l l))) (*.f64 t (pow.f64 (sin.f64 k) 2))) (neg.f64 (*.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2)))))

106.0ms

(*.f64 (/.f64 k (*.f64 (cos.f64 k) (*.f64 l l))) (*.f64 t (pow.f64 (sin.f64 k) 2)))

40.0ms

(/.f64 k (*.f64 (cos.f64 k) (*.f64 l l)))

rewrite100.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

390×	`prod-diff_binary64`
254×	`log1p-udef_binary64`
158×	`log1p-expm1-u_binary64`
158×	`expm1-log1p-u_binary64`
156×	`add-log-exp_binary64`

Counts

3 → 155

Calls

3 calls:

96.0ms

(fma.f64 k (*.f64 (/.f64 k (*.f64 (cos.f64 k) (*.f64 l l))) (*.f64 t (pow.f64 (sin.f64 k) 2))) (neg.f64 (*.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2)))))

96.0ms

(*.f64 (/.f64 k (*.f64 (cos.f64 k) (*.f64 l l))) (*.f64 t (pow.f64 (sin.f64 k) 2)))

96.0ms

(/.f64 k (*.f64 (cos.f64 k) (*.f64 l l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	75
1	400	61
2	4117	61
3	5221	61
0	0	0
1	0	0

simplify123.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

575×	`fma-def_binary64`
421×	`rules-4_binary64`
401×	`rules-13_binary64`
325×	`rules-14-rev_binary64`
273×	`rules-20_binary64`

Counts

251 → 185

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	82	2224
1	234	2210
2	960	2158
3	4843	2143
4	4965	2134
5	5097	2134

prune1.1s (3.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	463	6	469
Fresh	5	12	17
Picked	1	0	1
Done	1	0	1
Total	470	18	488

Error

2.1b

Counts

488 → 18

Alt Table

Status	Error	Program
	18.3b	(/.f64 2 (/.f64 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) l) (.f64 (cos.f64 k) l)))
	46.5b	(/.f64 2 (+.f64 (fma.f64 (.f64 (sin.f64 k) (sqrt.f64 t)) (.f64 (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2) (.f64 (sin.f64 k) (sqrt.f64 t))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	33.6b	(/.f64 2 (+.f64 (fma.f64 k (.f64 (pow.f64 (/.f64 (sqrt.f64 (/.f64 k (cos.f64 k))) l) 2) (.f64 t (pow.f64 (sin.f64 k) 2))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	45.6b	(/.f64 2 (+.f64 (fma.f64 k (pow.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 k (cos.f64 k))) l) (.f64 (sin.f64 k) (sqrt.f64 t))) 2) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	34.4b	(/.f64 2 (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 1 (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2))))
	18.1b	(/.f64 2 (+.f64 (fma.f64 k (/.f64 (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 k (cos.f64 k))) (.f64 l l)) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))))
	16.5b	(/.f64 2 (+.f64 (fma.f64 k (.f64 (/.f64 k (.f64 (cos.f64 k) (.f64 l l))) (+.f64 (fma.f64 (sin.f64 k) (.f64 (sin.f64 k) t) (neg.f64 (.f64 0 t))) (fma.f64 0 t (.f64 0 t)))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	29.0b	(/.f64 2 (.f64 (+.f64 (fma.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) (.f64 (tan.f64 k) (pow.f64 (.f64 (/.f64 t (pow.f64 (cbrt.f64 l) 2)) (cbrt.f64 (sin.f64 k))) 2)) (neg.f64 (.f64 0 (tan.f64 k)))) (fma.f64 0 (tan.f64 k) (.f64 0 (tan.f64 k)))) (pow.f64 (/.f64 k t) 2)))
	40.8b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k t) (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (/.f64 k t)) (neg.f64 (.f64 0 (pow.f64 (/.f64 k t) 2)))) (fma.f64 0 (pow.f64 (/.f64 k t) 2) (.f64 0 (pow.f64 (/.f64 k t) 2)))))
	34.5b	(/.f64 2 (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (pow.f64 (cbrt.f64 (pow.f64 (/.f64 k (*.f64 l (sqrt.f64 (cos.f64 k)))) 2)) 3)))
	47.2b	(/.f64 2 (.f64 (.f64 (*.f64 (pow.f64 (/.f64 (pow.f64 t 3/2) l) 2) (sin.f64 k)) (tan.f64 k)) (pow.f64 (/.f64 k t) 2)))
	45.7b	(/.f64 2 (pow.f64 (cbrt.f64 (pow.f64 (.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) (*.f64 (sin.f64 k) (sqrt.f64 t))) 2)) 3))
	34.5b	(/.f64 2 (+.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 t (pow.f64 (sin.f64 k) 2))) 2) (.f64 (cbrt.f64 (.f64 t (pow.f64 (sin.f64 k) 2))) (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2)) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	22.0b	(/.f64 2 (/.f64 (/.f64 (.f64 (.f64 k k) (.f64 t (pow.f64 (sin.f64 k) 2))) (cos.f64 k)) (.f64 l l)))
	44.6b	(/.f64 2 (+.f64 (.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 k (cos.f64 k))) l) (.f64 (sin.f64 k) (sqrt.f64 t))) (.f64 k (.f64 (/.f64 (sqrt.f64 (/.f64 k (cos.f64 k))) l) (.f64 (sin.f64 k) (sqrt.f64 t))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	18.1b	(/.f64 2 (+.f64 (fma.f64 k (/.f64 (.f64 k (.f64 t (pow.f64 (sin.f64 k) 2))) (.f64 (cos.f64 k) (pow.f64 l 2))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))))
	31.4b	(/.f64 2 (+.f64 (fma.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) (.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k))))) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	34.4b	(/.f64 2 (+.f64 (fma.f64 t (.f64 (pow.f64 (/.f64 k (.f64 l (sqrt.f64 (cos.f64 k)))) 2) (pow.f64 (sin.f64 k) 2)) (neg.f64 (.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2))))) (fma.f64 0 (.f64 t (pow.f64 (sin.f64 k) 2)) (.f64 0 (*.f64 t (pow.f64 (sin.f64 k) 2))))))

Compiler

Compiled 26391 to 14619 computations (44.6% saved)

regimes5.3s (15.9%)

Accuracy

Total 12.0b remaining (80.3%)

Threshold costs 0b (0%)

Counts

336 → 5

Compiler

Compiled 88162 to 59690 computations (32.3% saved)

bsearch1.0s (3.1%)

Steps

Iters	Range		Point
10	1.5167911106677958e+112	4.538739221865064e+127	4.429858786323863e+127
6	2.8474643804349697e-235	2.5624229356167864e-234	2.4761954081248927e-234
7	-5.197653113183199e-155	-1.5538694179975995e-156	-3.9559806813423186e-156
9	-8.468939629763175e+189	-3.0019865858619012e+184	-3.0320863962966904e+184

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	297
1	67	297
2	66	297

end474.0ms (1.4%)

Compiler: Compiled 1146 to 744 computations (35.1% saved)

Details

analyze3.6s (10.9%)

sample18.1s (54.7%)

simplify50.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0%)

series316.0ms (1%)

rewrite134.0ms (0.4%)

simplify103.0ms (0.3%)

prune471.0ms (1.4%)

localize15.0ms (0%)

series222.0ms (0.7%)

rewrite111.0ms (0.3%)

simplify38.0ms (0.1%)

prune623.0ms (1.9%)

localize16.0ms (0%)

series159.0ms (0.5%)

rewrite98.0ms (0.3%)

simplify79.0ms (0.2%)

prune529.0ms (1.6%)

localize18.0ms (0.1%)

series273.0ms (0.8%)

rewrite100.0ms (0.3%)

simplify123.0ms (0.4%)

prune1.1s (3.4%)

regimes5.3s (15.9%)

bsearch1.0s (3.1%)

simplify5.0ms (0%)

end474.0ms (1.4%)

Profiling