Details

analyze1.2s (9.8%)

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
1.6%	73.3%	25.1%	10
2.3%	60.1%	37.6%	11
4.7%	57.7%	37.6%	12
8.8%	53.6%	37.6%	13
10.2%	45.9%	43.8%	14

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample3.0s (23.9%)

Results

894.0ms	5541×	body	128	valid
617.0ms	1149×	body	1024	valid
438.0ms	825×	body	1024	invalid
363.0ms	924×	body	512	valid
222.0ms	1515×	body	128	invalid
210.0ms	518×	body	512	invalid
169.0ms	579×	body	256	valid
71.0ms	269×	body	256	invalid
42.0ms	63×	body	2048	valid

Compiler

Compiled 62 to 42 computations (32.3% saved)

preprocess39.0ms (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)

simplify25.0ms (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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

40.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.6b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))

Compiler

Compiled 116 to 75 computations (35.3% 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 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
✓	0.5b	(*.f64 (sqrt.f64 2) t)
✓	10.6b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
✓	19.6b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

series911.0ms (7.1%)

Counts

4 → 120

Calls

30 calls:

121.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))	l	0
113.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))	t	-inf
99.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))	x	0
92.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))	t	inf
91.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))	t	0

rewrite54.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
206×	`log1p-expm1-u_binary64`
206×	`expm1-log1p-u_binary64`
204×	`add-cbrt-cube_binary64`
200×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	105
1	437	105

Stop Event

1×	node limit

Counts

4 → 122

simplify209.0ms (1.6%)

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

242 → 279

prune790.0ms (6.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	269	10	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	270	10	280

Error

4.9b

Counts

280 → 10

Alt Table

Status	Error	Program
	37.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	59.9b	(/.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))))))
	59.9b	(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)))))
	60.0b	(*.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))))
	36.8b	(/.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))))))))
	40.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	59.7b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1))) l (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))) (+.f64 (.f64 (/.f64 (.f64 t t) l) (/.f64 x (+.f64 x -1))) (/.f64 (.f64 t t) (.f64 l (+.f64 x -1)))))))
	41.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
▶	28.7b	(/.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 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))))
	39.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (neg.f64 (.f64 l l)))))

Compiler

Compiled 42607 to 31628 computations (25.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	9.5b	(/.f64 (*.f64 l l) (pow.f64 x 3))
✓	15.5b	(/.f64 (.f64 t t) (.f64 x x))
✓	17.6b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	25.1b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))

series382.0ms (3%)

Counts

4 → 104

Calls

27 calls:

54.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))	l	inf
50.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))	l	-inf
45.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))	t	0
40.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))	l	0
39.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) (.f64 x x)) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 4 (/.f64 (.f64 t t) (pow.f64 x 3)) (fma.f64 2 (/.f64 (.f64 l l) (.f64 x x)) (fma.f64 2 (/.f64 (.f64 l l) (pow.f64 x 3)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))))))	t	-inf

rewrite40.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`log1p-expm1-u_binary64`
259×	`expm1-log1p-u_binary64`
256×	`add-cbrt-cube_binary64`
253×	`add-cube-cbrt_binary64`
253×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	110
1	563	99

Stop Event

1×	node limit

Counts

4 → 76

simplify131.0ms (1%)

Algorithm

1×	egg-herbie

Rules

661×	`fma-def_binary64`
410×	`associate-/r*_binary64`
315×	`times-frac_binary64`
291×	`associate-l_binary64`
246×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	533	11996
1	1728	9975

Stop Event

1×	node limit

Counts

180 → 136

prune425.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	135	11	146

Error

0.1b

Counts

146 → 11

Alt Table

Status	Error	Program
	54.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	36.8b	(/.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))))))))
	52.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (+.f64 (*.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l)))))))
	40.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	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 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))) 3/2)))
	37.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	54.5b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 t (/.f64 l t)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 (/.f64 t x) (/.f64 t x)) l)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) (pow.f64 x 3))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))))
▶	28.7b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))) 2))
	41.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	39.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (neg.f64 (.f64 l l)))))
	28.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))))

Compiler

Compiled 20890 to 14045 computations (32.8% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.0b	(fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))
✓	9.5b	(.f64 (.f64 l l) (pow.f64 x -3))
✓	17.6b	(.f64 (.f64 t t) (pow.f64 x -3))
✓	25.1b	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))

series455.0ms (3.6%)

Counts

4 → 116

Calls

30 calls:

50.0ms	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	l	inf
49.0ms	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	l	-inf
42.0ms	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	t	0
39.0ms	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	l	0
31.0ms	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	t	inf

rewrite45.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

268×	`log1p-expm1-u_binary64`
268×	`expm1-log1p-u_binary64`
265×	`add-log-exp_binary64`
264×	`add-cube-cbrt_binary64`
264×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	152
1	597	152

Stop Event

1×	node limit

Counts

4 → 59

simplify143.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-def_binary64`
413×	`associate-/r*_binary64`
326×	`times-frac_binary64`
247×	`associate-*r/_binary64`
215×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	557	13546
1	1825	11479

Stop Event

1×	node limit

Counts

175 → 142

prune398.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	141	12	153

Error

0.1b

Counts

153 → 12

Alt Table

Status	Error	Program
	54.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	36.8b	(/.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))))))))
	52.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (+.f64 (*.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l)))))))
	40.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	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 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))) 3/2)))
	37.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	55.3b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (neg.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))) 2))
	54.5b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 t (/.f64 l t)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 (/.f64 t x) (/.f64 t x)) l)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) (pow.f64 x 3))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))))
	56.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))) 2))
	41.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	39.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (neg.f64 (.f64 l l)))))
▶	28.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))))

Compiler

Compiled 21000 to 14864 computations (29.2% saved)

localize36.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	9.5b	(.f64 (.f64 l l) (pow.f64 x -3))
	17.6b	(.f64 (.f64 t t) (pow.f64 x -3))
	25.1b	(sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))
✓	25.9b	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))

series336.0ms (2.6%)

Counts

1 → 20

Calls

9 calls:

107.0ms	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	t	0
102.0ms	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	l	0
46.0ms	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	x	inf
42.0ms	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	x	-inf
13.0ms	(cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (*.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))))	x	0

rewrite31.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

267×	`log1p-expm1-u_binary64`
267×	`expm1-log1p-u_binary64`
264×	`add-cube-cbrt_binary64`
264×	`add-cbrt-cube_binary64`
264×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	72
1	595	72

Stop Event

1×	node limit

Counts

1 → 18

simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

605×	`fma-def_binary64`
419×	`associate-r_binary64`
320×	`associate-l_binary64`
203×	`associate-*r/_binary64`
190×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	450	7069
1	1484	6238

Stop Event

1×	node limit

Counts

38 → 52

prune689.0ms (5.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	182	12	194

Error

0.1b

Counts

194 → 12

Alt Table

Status	Error	Program
	54.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))
	36.8b	(/.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))))))))
	52.2b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 2 (+.f64 (*.f64 (/.f64 l x) (/.f64 l x)) (+.f64 (/.f64 l (/.f64 (pow.f64 x 3) l)) (/.f64 l (/.f64 x l)))))))
	40.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	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 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l))))))))) 3/2)))
	37.2b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	55.3b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (neg.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x)))))))) 2))
	54.5b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (/.f64 t (/.f64 l t)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) x)))) (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x)))))) (+.f64 (.f64 2 (/.f64 (.f64 (/.f64 t x) (/.f64 t x)) l)) (.f64 2 (/.f64 (/.f64 t (/.f64 l t)) (pow.f64 x 3))))) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))))
	56.6b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (sqrt.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))) 2))
	41.3b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	39.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (.f64 (sqrt.f64 (/.f64 (+.f64 x 1) (+.f64 x -1))) (hypot.f64 l (.f64 t (sqrt.f64 2)))) (neg.f64 (.f64 l l)))))
✓	28.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))) (cbrt.f64 (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 t (/.f64 x t)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (.f64 l l) (pow.f64 x -3)) (.f64 2 (fma.f64 t t (/.f64 l (/.f64 x l)))))))))))))

Compiler

Compiled 39086 to 25432 computations (34.9% saved)

regimes2.3s (17.7%)

Accuracy

Total 8.6b remaining (95.9%)

Threshold costs 0b (0%)

Counts

159 → 5

Compiler

Compiled 56440 to 36563 computations (35.2% saved)

bsearch516.0ms (4%)

Algorithm

4×	binary-search

Calls

4 calls:

210.0ms	t
145.0ms	t
79.0ms	t
69.0ms	t

Steps

Iters	Point		Range
2.2762156236312662e+86	∈ [	2.0462799880650105e+84	,	2.3092605058956445e+86	]
-3.555419331691467e-260	∈ [	-3.611797466858081e-260	,	-1.5142158246706247e-281	]
-1.0337511219279627e-137	∈ [	-7.653312618459714e-137	,	-1.0216629075878398e-137	]
-1.571665268792021e+71	∈ [	-1.5956685620324244e+71	,	-7.094999967271411e+67	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
3×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	250
1	63	250
2	72	250
3	77	250
4	79	250

Stop Event

1×

saturated

end386.0ms (3%)

Stop Event

1×

fuel

Compiler

Compiled 866 to 579 computations (33.1% saved)

Details

analyze1.2s (9.8%)

sample3.0s (23.9%)

preprocess39.0ms (0.3%)

simplify25.0ms (0.2%)

prune3.0ms (0%)

localize15.0ms (0.1%)

series911.0ms (7.1%)

rewrite54.0ms (0.4%)

simplify209.0ms (1.6%)

prune790.0ms (6.2%)

localize26.0ms (0.2%)

series382.0ms (3%)

rewrite40.0ms (0.3%)

simplify131.0ms (1%)

prune425.0ms (3.3%)

localize33.0ms (0.3%)

series455.0ms (3.6%)

rewrite45.0ms (0.4%)

simplify143.0ms (1.1%)

prune398.0ms (3.1%)

localize36.0ms (0.3%)

series336.0ms (2.6%)

rewrite31.0ms (0.2%)

simplify82.0ms (0.6%)

prune689.0ms (5.4%)

regimes2.3s (17.7%)

bsearch516.0ms (4%)

simplify8.0ms (0.1%)

end386.0ms (3%)

Profiling