Details

analyze1.1s (8.8%)

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
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample3.1s (25.2%)

Results

876.0ms	5492×	body	128	valid
642.0ms	1180×	body	1024	valid
458.0ms	848×	body	1024	invalid
405.0ms	973×	body	512	valid
249.0ms	1619×	body	128	invalid
218.0ms	530×	body	512	invalid
150.0ms	552×	body	256	valid
73.0ms	275×	body	256	invalid
40.0ms	59×	body	2048	valid

Compiler

Compiled 62 to 42 computations (32.3% saved)

preprocess40.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

443×	`fma-neg_binary64`
411×	`fma-def_binary64`
304×	`times-frac_binary64`
276×	`associate-/l*_binary64`
225×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	156
1	140	156
2	385	156
3	959	156
4	2234	156
5	4312	156
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify23.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary64`
506×	`fma-neg_binary64`
403×	`cancel-sign-sub-inv_binary64`
259×	`distribute-rgt-neg-in_binary64`
215×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	48	39
2	117	39
3	267	39
4	618	39
5	1427	39
6	3153	39

Stop Event

1×	node limit

Counts

1 → 2

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

41.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	41.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))

Compiler

Compiled 114 to 75 computations (34.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	10.1b	(fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l)))
✓	22.4b	(sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l))))

series847.0ms (6.8%)

Counts

4 → 120

Calls

30 calls:

115.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))	t	-inf
115.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))	l	0
93.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))	t	inf
89.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))	x	0
88.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (.f64 l (neg.f64 l)))))	t	0

rewrite47.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

208×	`add-sqr-sqrt_binary64`
202×	`*-un-lft-identity_binary64`
202×	`pow1_binary64`
191×	`add-cbrt-cube_binary64`
190×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	105
1	420	99

Stop Event

1×	node limit

Counts

4 → 104

simplify210.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

632×	`*-commutative_binary64`
385×	`fma-def_binary64`
342×	`associate-+r+_binary64`
278×	`associate-r_binary64`
225×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28688

Stop Event

1×	node limit

Counts

224 → 261

prune970.0ms (7.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	250	11	261
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	251	11	262

Error

4.2b

Counts

262 → 11

Alt Table

Status	Error	Program
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	39.9b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1))))))))
	60.4b	(neg.f64 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))) (/.f64 t (/.f64 l (sqrt.f64 2)))))
	60.3b	(*.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))) (/.f64 t (/.f64 l (sqrt.f64 2))))
	60.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1))))))
	60.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	45.9b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (+.f64 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) (pow.f64 x 2)))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (pow.f64 t 3) (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2))))) (+.f64 (.f64 2 (/.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))) (.f64 2 (/.f64 (pow.f64 l 2) (.f64 t (.f64 (pow.f64 (sqrt.f64 2) 3) (pow.f64 x 2)))))))))
	40.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	37.5b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (.f64 t t) (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	35.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
▶	32.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))

Compiler

Compiled 41517 to 30976 computations (25.4% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	6.9b	(/.f64 (*.f64 t t) x)
✓	9.4b	(/.f64 (.f64 l l) (.f64 x x))
✓	15.8b	(/.f64 (.f64 t t) (.f64 x x))
✓	27.5b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))

series202.0ms (1.6%)

Counts

4 → 108

Calls

27 calls:

22.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))	t	0
22.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))	l	-inf
22.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))	l	0
21.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))	l	inf
17.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))	t	inf

rewrite46.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
209×	`*-un-lft-identity_binary64`
209×	`pow1_binary64`
198×	`add-exp-log_binary64`
198×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	81
1	426	67

Stop Event

1×	node limit

Counts

4 → 121

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

493×	`fma-def_binary64`
289×	`associate-/r*_binary64`
277×	`associate-r_binary64`
249×	`associate-l_binary64`
221×	`times-frac_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	417	7585
1	1348	6486

Stop Event

1×	node limit

Counts

229 → 188

prune324.0ms (2.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	179	9	188
Fresh	5	5	10
Picked	0	1	1
Done	0	0	0
Total	184	15	199

Error

0.2b

Counts

199 → 15

Alt Table

Status	Error	Program
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 3/2)))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2)))))))
▶	28.4b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2))
	39.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2))) (neg.f64 t)))
	40.3b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	43.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))
	37.5b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (.f64 t t) (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	56.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))) (neg.f64 l)))
✓	32.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	54.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	34.6b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2))))))
	60.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	35.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	34.3b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))

Compiler

Compiled 15665 to 9544 computations (39.1% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)
✓	0.5b	(fma.f64 t t (/.f64 l (/.f64 x l)))
✓	4.8b	(fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))
✓	28.2b	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4)

series677.0ms (5.4%)

Counts

4 → 144

Calls

36 calls:

69.0ms	(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)	l	-inf
66.0ms	(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)	l	inf
61.0ms	(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)	t	0
52.0ms	(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)	l	0
48.0ms	(pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2)	t	-inf

rewrite43.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

224×	`add-sqr-sqrt_binary64`
224×	`pow1_binary64`
220×	`*-un-lft-identity_binary64`
213×	`add-log-exp_binary64`
213×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	139
1	480	138

Stop Event

1×	node limit

Counts

4 → 69

simplify236.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

362×	`*-commutative_binary64`
258×	`+-commutative_binary64`
202×	`fma-def_binary64`
188×	`associate-+r+_binary64`
135×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	947	21215
1	3670	19846

Stop Event

1×	node limit

Counts

213 → 221

prune611.0ms (4.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	219	2	221
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	220	16	236

Error

0.2b

Counts

236 → 16

Alt Table

Status	Error	Program
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 3/2)))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2)))))))
✓	28.4b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2))
	39.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2))) (neg.f64 t)))
	56.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 (.f64 2 (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 2))))) (*.f64 2 (log.f64 (/.f64 1 l)))))) 2))
	60.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	42.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 2 (log.f64 (/.f64 -1 t)))))) 2))
	43.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))
	37.5b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (.f64 t t) (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	56.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))) (neg.f64 l)))
✓	32.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	54.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	34.6b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2))))))
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	35.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
▶	34.3b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))

Compiler

Compiled 32444 to 23536 computations (27.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))
	0.4b	(*.f64 (sqrt.f64 2) t)
✓	3.6b	(/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l))
✓	3.9b	(/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)

series139.0ms (1.1%)

Counts

3 → 108

Calls

27 calls:

13.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))	l	inf
11.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))	t	0
11.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))	l	-inf
10.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))	t	-inf
7.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))	t	inf

rewrite44.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

177×	`add-sqr-sqrt_binary64`
174×	`*-un-lft-identity_binary64`
174×	`pow1_binary64`
163×	`add-exp-log_binary64`
163×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	68
1	352	68

Stop Event

1×	node limit

Counts

3 → 129

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
331×	`unswap-sqr_binary64`
254×	`cancel-sign-sub-inv_binary64`
221×	`associate-r_binary64`
218×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	4525
1	592	3970
2	2775	3896

Stop Event

1×	node limit

Counts

237 → 172

prune227.0ms (1.8%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	13	13
Picked	0	1	1
Done	0	2	2
Total	187	16	203

Error

0.2b

Counts

203 → 16

Alt Table

Status	Error	Program
	37.6b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 3/2)))
	38.3b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2)))))))
✓	28.4b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 1/4) 2))
	39.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2))) (neg.f64 t)))
	56.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 (.f64 2 (/.f64 1 x)) (.f64 2 (/.f64 1 (pow.f64 x 2))))) (*.f64 2 (log.f64 (/.f64 1 l)))))) 2))
	60.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	42.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (exp.f64 (.f64 1/4 (-.f64 (log.f64 (+.f64 2 (+.f64 (.f64 4 (/.f64 1 x)) (.f64 4 (/.f64 1 (pow.f64 x 2)))))) (*.f64 2 (log.f64 (/.f64 -1 t)))))) 2))
	43.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))) 2))) (sqrt.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))
	37.5b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (.f64 t t) (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	56.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))) (neg.f64 l)))
✓	32.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	54.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	34.6b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 4 (.f64 x x)) (+.f64 (/.f64 4 x) 2)))) (+.f64 (.f64 (/.f64 l x) (/.f64 l t)) (/.f64 (.f64 (/.f64 l x) (/.f64 l x)) t))) (.f64 t (sqrt.f64 (+.f64 (/.f64 4 (*.f64 x x)) (+.f64 (/.f64 4 x) 2))))))
	36.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	35.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
✓	34.3b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 l (/.f64 (.f64 (.f64 x t) (sqrt.f64 2)) l)))))

Compiler

Compiled 7938 to 5472 computations (31.1% saved)

regimes1.8s (14.8%)

Accuracy

Total 8.2b remaining (94.9%)

Threshold costs 0b (0%)

Counts

101 → 7

Compiler

Compiled 29637 to 21315 computations (28.1% saved)

bsearch979.0ms (7.9%)

Algorithm

6×	binary-search

Calls

6 calls:

240.0ms	t
195.0ms	t
182.0ms	t
175.0ms	t
93.0ms	t

Steps

Iters	Point		Range
1.7505159449100466e+61	∈ [	5.694711511864425e+58	,	1.771214718454333e+61	]
2.898770924274869e-166	∈ [	2.839046648729363e-166	,	1.0747341396254306e-152	]
-1.1119314911646242e-301	∈ [	-1.3175102798881419e-284	,	-1.0860500822955934e-301	]
-1.1070675823535772e-218	∈ [	-1.1230928926858213e-218	,	-5.188636030229106e-223	]
-4.598917439395751e-161	∈ [	-4.5396632039609245e-156	,	-4.54101843365594e-161	]
-7.313146234677325	∈ [	-7.403080977117122	,	-0.13686834101652998	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify16.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

26×	`*-commutative_binary64`
19×	`+-commutative_binary64`
13×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	81	389
1	111	389
2	130	389
3	147	389
4	169	389
5	187	389
6	197	389
7	202	389
8	203	389

Stop Event

1×

saturated

end458.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 1102 to 731 computations (33.7% saved)

Iter	Nodes	Cost
0	81	389
1	111	389
2	130	389
3	147	389
4	169	389
5	187	389
6	197	389
7	202	389
8	203	389

Iter	Nodes	Cost
0	81	389
1	111	389
2	130	389
3	147	389
4	169	389
5	187	389
6	197	389
7	202	389
8	203	389

Details

analyze1.1s (8.8%)

sample3.1s (25.2%)

preprocess40.0ms (0.3%)

simplify23.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series847.0ms (6.8%)

rewrite47.0ms (0.4%)

simplify210.0ms (1.7%)

prune970.0ms (7.8%)

localize21.0ms (0.2%)

series202.0ms (1.6%)

rewrite46.0ms (0.4%)

simplify92.0ms (0.7%)

prune324.0ms (2.6%)

localize26.0ms (0.2%)

series677.0ms (5.4%)

rewrite43.0ms (0.3%)

simplify236.0ms (1.9%)

prune611.0ms (4.9%)

localize14.0ms (0.1%)

series139.0ms (1.1%)

rewrite44.0ms (0.4%)

simplify77.0ms (0.6%)

prune227.0ms (1.8%)

regimes1.8s (14.8%)

bsearch979.0ms (7.9%)

simplify16.0ms (0.1%)

end458.0ms (3.7%)

Profiling

Iter	Nodes	Cost
0	81	389
1	111	389
2	130	389
3	147	389
4	169	389
5	187	389
6	197	389
7	202	389
8	203	389