Details

analyze2.9s (19.8%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
1.6%	98.3%	0.1%	8
2.3%	97.5%	0.1%	9
7.4%	90.9%	1.7%	10
9.2%	87.4%	3.5%	11
11.7%	83.5%	4.8%	12
15.2%	76%	8.8%	13
16.4%	72%	11.6%	14

Compiler

Compiled 29 to 22 computations (24.1% saved)

sample5.3s (36.2%)

Results

2.7s	2779×	body	1024	valid
893.0ms	3657×	body	128	valid
868.0ms	1240×	body	512	valid
379.0ms	1561×	body	128	invalid
257.0ms	574×	body	256	valid
102.0ms	147×	body	512	invalid
52.0ms	55×	body	1024	invalid
43.0ms	99×	body	256	invalid
9.0ms	6×	body	2048	valid

Compiler

Compiled 58 to 44 computations (24.1% saved)

preprocess37.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

924×	`times-frac_binary64`
389×	`associate-l_binary64`
386×	`associate-*l/_binary64`
361×	`associate-r_binary64`
301×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	152
1	171	140
2	687	140
3	4497	140
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 28 to 21 computations (25% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

428×	`associate-/r/_binary64`
398×	`associate-/r*_binary64`
395×	`fma-def_binary64`
380×	`distribute-rgt-out_binary64`
325×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	55	35
2	193	35
3	1146	35
4	4817	35

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

29.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	34.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
▶	31.4b	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))

Status

Error

Program

34.0b

(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))

▶

31.4b

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

Compiler

Compiled 159 to 114 computations (28.3% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.6b	(*.f64 (pow.f64 t 3) (sin.f64 k))
✓	6.9b	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
✓	7.3b	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)
✓	16.5b	(/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))))

series532.0ms (3.6%)

Counts

4 → 100

Calls

30 calls:

64.0ms	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)	l	inf
63.0ms	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)	l	-inf
55.0ms	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))	l	0
50.0ms	(.f64 l (.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))	l	inf
49.0ms	(.f64 (/.f64 (/.f64 2 (.f64 (pow.f64 t 3) (sin.f64 k))) (*.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l)	l	0

rewrite45.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

201×	`add-sqr-sqrt_binary64`
191×	`log1p-expm1-u_binary64`
191×	`expm1-log1p-u_binary64`
188×	`add-cbrt-cube_binary64`
187×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	105
1	408	105

Stop Event

1×	node limit

Counts

4 → 93

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

521×	`times-frac_binary64`
379×	`associate-/l*_binary64`
372×	`associate-/r*_binary64`
286×	`associate-r_binary64`
236×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	334	6037
1	1253	5945

Stop Event

1×	node limit

Counts

193 → 183

prune295.0ms (2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	170	13	183
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	171	14	185

Error

10.7b

Counts

185 → 14

Alt Table

Status	Error	Program
	31.5b	(.f64 l (.f64 (.f64 (/.f64 2 (pow.f64 (cbrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) 2)) (/.f64 (/.f64 1 (.f64 (pow.f64 t 3) (sin.f64 k))) (cbrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))) l))
▶	25.9b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	26.2b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (tan.f64 k))) l))
	35.4b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	31.0b	(.f64 l (log.f64 (pow.f64 (exp.f64 l) (/.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (.f64 (tan.f64 k) (sin.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	38.6b	(.f64 l (fma.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (/.f64 l t) (pow.f64 (sin.f64 k) 2))) (.f64 (.f64 (/.f64 (cos.f64 k) (pow.f64 k 4)) (/.f64 (.f64 t l) (pow.f64 (sin.f64 k) 2))) -4)))
	26.4b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	34.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
	30.9b	(.f64 l (.f64 (/.f64 2 (.f64 k (.f64 k t))) (/.f64 (*.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2))))
	29.7b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	54.2b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 (sqrt.f64 (sin.f64 k)) (pow.f64 t 3/2)) 2)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	29.2b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	35.5b	(.f64 2 (/.f64 (/.f64 (/.f64 (.f64 l l) (/.f64 (*.f64 k k) (cos.f64 k))) t) (pow.f64 (sin.f64 k) 2)))
	33.4b	(.f64 l (.f64 (.f64 (/.f64 2 (.f64 k k)) (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) l))

Compiler

Compiled 7686 to 4714 computations (38.7% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.7b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	6.9b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
✓	7.7b	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))
✓	9.7b	(*.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2))

series544.0ms (3.7%)

Counts

4 → 100

Calls

30 calls:

62.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	-inf
62.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	-inf
61.0ms	(/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	inf
60.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	0
60.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	inf

rewrite58.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

209×	`add-sqr-sqrt_binary64`
197×	`log1p-expm1-u_binary64`
197×	`expm1-log1p-u_binary64`
194×	`add-cbrt-cube_binary64`
194×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	118
1	430	118

Stop Event

1×	node limit

Counts

4 → 85

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

434×	`times-frac_binary64`
316×	`associate-/l*_binary64`
283×	`associate-/r*_binary64`
268×	`fma-neg_binary64`
257×	`associate-r_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	269	5124
1	990	5052
2	4593	5052

Stop Event

1×	node limit

Counts

185 → 162

prune351.0ms (2.4%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	154	8	162
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	156	20	176

Error

10.6b

Counts

176 → 20

Alt Table

Status	Error	Program
	26.2b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (tan.f64 k))) l))
	35.4b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	26.4b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	25.9b	(.f64 l (.f64 2 (pow.f64 (cbrt.f64 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))) 3)))
	47.2b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) (sqrt.f64 (cos.f64 k)))) 2) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	33.1b	(.f64 l (.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	34.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
	31.0b	(.f64 l (log.f64 (pow.f64 (exp.f64 l) (/.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (.f64 (tan.f64 k) (sin.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
	38.6b	(.f64 l (fma.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 (/.f64 l t) (pow.f64 (sin.f64 k) 2))) (.f64 (.f64 (/.f64 (cos.f64 k) (pow.f64 k 4)) (/.f64 (.f64 t l) (pow.f64 (sin.f64 k) 2))) -4)))
▶	24.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	29.2b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	30.2b	(.f64 2 (/.f64 (.f64 l l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2))))))
	31.5b	(.f64 l (.f64 (.f64 (/.f64 2 (pow.f64 (cbrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) 2)) (/.f64 (/.f64 1 (.f64 (pow.f64 t 3) (sin.f64 k))) (cbrt.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))))) l))
	26.0b	(pow.f64 (cbrt.f64 (.f64 l (/.f64 (.f64 2 l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2))))))) 3)
	30.9b	(.f64 l (.f64 (/.f64 2 (.f64 k (.f64 k t))) (/.f64 (*.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2))))
	29.7b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	39.8b	(*.f64 (/.f64 l (/.f64 (pow.f64 t 3) l)) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))
	32.8b	(.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (/.f64 (.f64 t (pow.f64 (sin.f64 k) 2)) l))))
	35.5b	(.f64 2 (/.f64 (/.f64 (/.f64 (.f64 l l) (/.f64 (*.f64 k k) (cos.f64 k))) t) (pow.f64 (sin.f64 k) 2)))
	33.4b	(.f64 l (.f64 (.f64 (/.f64 2 (.f64 k k)) (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) l))

Compiler

Compiled 8224 to 4867 computations (40.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.7b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	6.9b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
✓	7.7b	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))
✓	9.7b	(cbrt.f64 (pow.f64 (sin.f64 k) 2))

series842.0ms (5.7%)

Counts

3 → 74

Calls

21 calls:

106.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	0
105.0ms	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	-inf
100.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	-inf
100.0ms	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	inf
99.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	inf

rewrite45.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

226×	`add-sqr-sqrt_binary64`
214×	`log1p-expm1-u_binary64`
214×	`expm1-log1p-u_binary64`
212×	`add-cbrt-cube_binary64`
210×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	108
1	470	100

Stop Event

1×	node limit

Counts

3 → 60

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

523×	`associate-/r/_binary64`
350×	`times-frac_binary64`
350×	`fma-def_binary64`
287×	`cancel-sign-sub-inv_binary64`
242×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	4030
1	644	3982
2	3004	3790

Stop Event

1×	node limit

Counts

134 → 109

prune313.0ms (2.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	6	13	19
Picked	0	1	1
Done	0	0	0
Total	135	17	152

Error

10.2b

Counts

152 → 17

Alt Table

Status	Error	Program
	24.2b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (cos.f64 k)) (pow.f64 t 3)) (.f64 (/.f64 k (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) k)))))
	35.4b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	47.2b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) (sqrt.f64 (cos.f64 k)))) 2) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	33.1b	(.f64 l (.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	34.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
	31.0b	(.f64 l (log.f64 (pow.f64 (exp.f64 l) (/.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (.f64 (tan.f64 k) (sin.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
✓	24.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
▶	17.0b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	30.9b	(.f64 l (.f64 (/.f64 2 (.f64 k (.f64 k t))) (/.f64 (*.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2))))
	29.2b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	30.2b	(.f64 2 (/.f64 (.f64 l l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2))))))
	26.0b	(pow.f64 (cbrt.f64 (.f64 l (/.f64 (.f64 2 l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2))))))) 3)
	26.4b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	29.7b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	39.8b	(*.f64 (/.f64 l (/.f64 (pow.f64 t 3) l)) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))
	35.5b	(.f64 2 (/.f64 (/.f64 (/.f64 (.f64 l l) (/.f64 (*.f64 k k) (cos.f64 k))) t) (pow.f64 (sin.f64 k) 2)))
	36.7b	(.f64 l (.f64 2 (/.f64 (/.f64 l t) (pow.f64 k 4))))

Compiler

Compiled 6442 to 3646 computations (43.4% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.2b	(.f64 (/.f64 (.f64 k k) (cos.f64 k)) (*.f64 t (pow.f64 (sin.f64 k) 2)))
	3.7b	(*.f64 t (pow.f64 (sin.f64 k) 2))
✓	6.9b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
✓	7.7b	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))

series854.0ms (5.8%)

Counts

3 → 90

Calls

24 calls:

114.0ms	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	inf
113.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	inf
109.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	0
105.0ms	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))	l	-inf
105.0ms	(/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))	l	-inf

rewrite39.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

232×	`add-sqr-sqrt_binary64`
223×	`log1p-expm1-u_binary64`
223×	`expm1-log1p-u_binary64`
219×	`add-cbrt-cube_binary64`
217×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	120
1	491	112

Stop Event

1×	node limit

Counts

3 → 58

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

499×	`fma-def_binary64`
350×	`times-frac_binary64`
287×	`cancel-sign-sub-inv_binary64`
242×	`associate-/l*_binary64`
235×	`associate-/l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	182	4454
1	687	4403
2	3144	4200

Stop Event

1×	node limit

Counts

148 → 116

prune303.0ms (2.1%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	1	14	15
Picked	0	1	1
Done	0	1	1
Total	137	19	156

Error

9.7b

Counts

156 → 19

Alt Table

Status	Error	Program
	24.2b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (.f64 (/.f64 (pow.f64 (sin.f64 k) 2) (cos.f64 k)) (pow.f64 t 3)) (.f64 (/.f64 k (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2))) k)))))
	35.4b	(.f64 l (.f64 (/.f64 (cos.f64 k) (pow.f64 t 3)) (.f64 (/.f64 (/.f64 l (pow.f64 (sin.f64 k) 2)) (+.f64 2 (.f64 (/.f64 k t) (/.f64 k t)))) 2)))
	31.5b	(.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (.f64 t (/.f64 (pow.f64 (sin.f64 k) 2) l)))))
	47.2b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (sin.f64 k) (/.f64 (pow.f64 t 3/2) (sqrt.f64 (cos.f64 k)))) 2) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	33.1b	(.f64 l (.f64 2 (.f64 (/.f64 (cos.f64 k) (.f64 k k)) (/.f64 l (*.f64 t (pow.f64 (sin.f64 k) 2))))))
	34.0b	(/.f64 2 (.f64 (.f64 (.f64 (/.f64 (pow.f64 t 3) (.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1)))
	38.7b	(.f64 2 (/.f64 (/.f64 (.f64 l l) (pow.f64 k 4)) t))
	31.0b	(.f64 l (log.f64 (pow.f64 (exp.f64 l) (/.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (.f64 (tan.f64 k) (sin.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2))))))
✓	24.1b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (cbrt.f64 (pow.f64 (sin.f64 k) 2)) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
✓	17.0b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (pow.f64 (.f64 (pow.f64 (cbrt.f64 (sin.f64 k)) 2) (/.f64 t (cbrt.f64 (cos.f64 k)))) 3) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2)))))))
	30.9b	(.f64 l (.f64 (/.f64 2 (.f64 k (.f64 k t))) (/.f64 (*.f64 (cos.f64 k) l) (pow.f64 (sin.f64 k) 2))))
	29.2b	(.f64 l (.f64 (/.f64 (/.f64 2 (pow.f64 (.f64 t (cbrt.f64 (sin.f64 k))) 3)) (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	30.2b	(.f64 2 (/.f64 (.f64 l l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2))))))
	26.0b	(pow.f64 (cbrt.f64 (.f64 l (/.f64 (.f64 2 l) (fma.f64 2 (.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (.f64 (/.f64 (.f64 k k) (cos.f64 k)) (.f64 t (pow.f64 (sin.f64 k) 2))))))) 3)
	26.4b	(.f64 l (.f64 (.f64 (/.f64 (pow.f64 (/.f64 (cbrt.f64 2) (.f64 t (cbrt.f64 (sin.f64 k)))) 2) (tan.f64 k)) (/.f64 (/.f64 (cbrt.f64 2) (*.f64 t (cbrt.f64 (sin.f64 k)))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))) l))
	24.2b	(.f64 l (.f64 2 (/.f64 l (fma.f64 2 (*.f64 (/.f64 (pow.f64 t 3) (cos.f64 k)) (pow.f64 (sin.f64 k) 2)) (/.f64 k (/.f64 (/.f64 (/.f64 (cos.f64 k) t) (pow.f64 (sin.f64 k) 2)) k))))))
	29.7b	(.f64 l (/.f64 1 (/.f64 (.f64 (tan.f64 k) (+.f64 2 (pow.f64 (/.f64 k t) 2))) (*.f64 (/.f64 (/.f64 2 (pow.f64 t 3)) (sin.f64 k)) l))))
	39.8b	(*.f64 (/.f64 l (/.f64 (pow.f64 t 3) l)) (/.f64 (cos.f64 k) (pow.f64 (sin.f64 k) 2)))
	36.7b	(.f64 l (.f64 2 (/.f64 (/.f64 l t) (pow.f64 k 4))))

Compiler

Compiled 6281 to 3475 computations (44.7% saved)

regimes1.3s (9.1%)

Accuracy

Total 4.9b remaining (34.5%)

Threshold costs 0b (0%)

Counts

101 → 4

Compiler

Compiled 16691 to 11950 computations (28.4% saved)

bsearch6.0ms (0%)

Algorithm

3×	left-value

Calls

3 calls:

0.0ms

(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

0.0ms

(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

0.0ms

(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 (+.f64 1 (pow.f64 (/.f64 k t) 2)) 1))

Steps

Iters

Point

Range

#hash((type . real) (value . +inf))

∈ [

#hash((type . real) (value . +inf))

#hash((type . real) (value . NaN))

]

14593031620471792.0

∈ [

14593031620471792.0

2.987227160703109e+63

]

-70969323.52844514

∈ [

-70969323.52844514

-4.859022675140389e-246

]

Compiler

Compiled 26 to 19 computations (26.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
3×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	293
1	81	293

Stop Event

1×

saturated

end405.0ms (2.8%)

Stop Event

1×

fuel

Compiler

Compiled 929 to 601 computations (35.3% saved)

Details

analyze2.9s (19.8%)

sample5.3s (36.2%)

preprocess37.0ms (0.2%)

simplify23.0ms (0.2%)

prune7.0ms (0%)

localize16.0ms (0.1%)

series532.0ms (3.6%)

rewrite45.0ms (0.3%)

simplify77.0ms (0.5%)

prune295.0ms (2%)

localize22.0ms (0.1%)

series544.0ms (3.7%)

rewrite58.0ms (0.4%)

simplify92.0ms (0.6%)

prune351.0ms (2.4%)

localize22.0ms (0.2%)

series842.0ms (5.7%)

rewrite45.0ms (0.3%)

simplify79.0ms (0.5%)

prune313.0ms (2.1%)

localize23.0ms (0.2%)

series854.0ms (5.8%)

rewrite39.0ms (0.3%)

simplify95.0ms (0.6%)

prune303.0ms (2.1%)

regimes1.3s (9.1%)

bsearch6.0ms (0%)

simplify4.0ms (0%)

end405.0ms (2.8%)

Profiling