Details

analyze1.1s (6.6%)

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)

sample3.2s (18.6%)

Results

880.0ms	5509×	body	128	valid
660.0ms	1205×	body	1024	valid
450.0ms	875×	body	1024	invalid
388.0ms	916×	body	512	valid
253.0ms	1584×	body	128	invalid
231.0ms	543×	body	512	invalid
159.0ms	561×	body	256	valid
77.0ms	293×	body	256	invalid
43.0ms	65×	body	2048	valid

Compiler

Compiled 62 to 42 computations (32.3% saved)

preprocess45.0ms (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 (0.1%)

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

prune5.0ms (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

42.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	42.1b	(/.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))))
▶	42.1b	(/.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)))))

Status

Error

Program

42.1b

(/.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))))

▶

42.1b

(/.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 174 to 115 computations (33.9% saved)

localize16.0ms (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)))))
✓	0.5b	(*.f64 (sqrt.f64 2) t)
✓	11.1b	(fma.f64 (/.f64 (+.f64 x 1) (+.f64 x -1)) (fma.f64 2 (.f64 t t) (.f64 l l)) (*.f64 l (neg.f64 l)))
✓	23.4b	(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))))

series882.0ms (5.2%)

Counts

4 → 120

Calls

30 calls:

120.0ms	(/.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
116.0ms	(/.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
95.0ms	(/.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
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)))))	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

rewrite49.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

199×	`add-sqr-sqrt_binary64`
190×	`log1p-expm1-u_binary64`
190×	`expm1-log1p-u_binary64`
187×	`add-cbrt-cube_binary64`
185×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	105
1	420	99

Stop Event

1×	node limit

Counts

4 → 104

simplify206.0ms (1.2%)

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

prune833.0ms (4.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	249	12	261
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	251	12	263

Error

4.5b

Counts

263 → 12

Alt Table

Status	Error	Program
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	58.9b	(/.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))))))
	42.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (fma.f64 2 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (fma.f64 2 (/.f64 (.f64 t t) (+.f64 x -1)) (+.f64 (/.f64 (.f64 l l) (/.f64 (+.f64 x -1) x)) (/.f64 (.f64 l l) (+.f64 x -1))))) (.f64 l l))))
	39.3b	(/.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))))))))
▶	32.9b	(/.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))))))))))
	38.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (+.f64 x -1)) (*.f64 2 (/.f64 x (+.f64 x -1)))))))
	47.3b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (+.f64 (/.f64 (.f64 l l) (.f64 (.f64 t (sqrt.f64 2)) (.f64 x x))) (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (sqrt.f64 2)))) (fma.f64 3 (/.f64 (/.f64 (pow.f64 l 4) (pow.f64 t 3)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 4 (/.f64 t (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (fma.f64 6 (/.f64 (.f64 l l) (.f64 (.f64 t (pow.f64 (sqrt.f64 2) 5)) (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 (.f64 l l) t) (.f64 x (sqrt.f64 2))) (fma.f64 1/2 (/.f64 (/.f64 (pow.f64 l 6) (pow.f64 t 5)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 t (sqrt.f64 2) (.f64 2 (+.f64 (/.f64 t (.f64 (.f64 x x) (sqrt.f64 2))) (/.f64 t (.f64 (pow.f64 x 3) (sqrt.f64 2))))))))))))) (fma.f64 4 (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (fma.f64 2 (/.f64 (/.f64 (.f64 l l) t) (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))) (fma.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (.f64 x x))) (fma.f64 2 (/.f64 t (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (*.f64 4 (/.f64 (/.f64 t (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))))))))))
	39.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	37.0b	(/.f64 (.f64 (sqrt.f64 2) t) (+.f64 (.f64 t (sqrt.f64 2)) (+.f64 (.f64 2 (/.f64 t (.f64 (sqrt.f64 2) x))) (/.f64 (pow.f64 l 2) (.f64 t (.f64 (sqrt.f64 2) x))))))
	59.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	58.9b	(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)))))
	59.0b	(*.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))))

Compiler

Compiled 41919 to 31226 computations (25.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	11.5b	(/.f64 (.f64 l l) (.f64 x x))
✓	18.9b	(/.f64 (.f64 t t) (.f64 x x))
✓	19.8b	(/.f64 (*.f64 t t) (pow.f64 x 3))
✓	28.1b	(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)))))))))

series385.0ms (2.3%)

Counts

4 → 104

Calls

27 calls:

52.0ms	(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
46.0ms	(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
41.0ms	(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
37.0ms	(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

rewrite41.0ms (0.2%)

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	96

Stop Event

1×	node limit

Counts

4 → 79

simplify128.0ms (0.8%)

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

183 → 138

prune423.0ms (2.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	135	15	150

Error

0.4b

Counts

150 → 15

Alt Table

Status	Error	Program
	40.2b	(/.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)))
	35.3b	(/.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 (sqrt.f64 2) (.f64 x t)) l)))))
▶	33.0b	(/.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))
	51.7b	(/.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)))))))
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	33.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (pow.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)))))))))) 2) 1/2) (pow.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)))))))))) 1/2)))
	39.3b	(/.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))))))))
	55.1b	(/.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))))))))))
	42.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (fma.f64 2 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (fma.f64 2 (/.f64 (.f64 t t) (+.f64 x -1)) (+.f64 (/.f64 (.f64 l l) (/.f64 (+.f64 x -1) x)) (/.f64 (.f64 l l) (+.f64 x -1))))) (.f64 l l))))
	54.9b	(/.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)))))))
	47.3b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (+.f64 (/.f64 (.f64 l l) (.f64 (.f64 t (sqrt.f64 2)) (.f64 x x))) (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (sqrt.f64 2)))) (fma.f64 3 (/.f64 (/.f64 (pow.f64 l 4) (pow.f64 t 3)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 4 (/.f64 t (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (fma.f64 6 (/.f64 (.f64 l l) (.f64 (.f64 t (pow.f64 (sqrt.f64 2) 5)) (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 (.f64 l l) t) (.f64 x (sqrt.f64 2))) (fma.f64 1/2 (/.f64 (/.f64 (pow.f64 l 6) (pow.f64 t 5)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 t (sqrt.f64 2) (.f64 2 (+.f64 (/.f64 t (.f64 (.f64 x x) (sqrt.f64 2))) (/.f64 t (.f64 (pow.f64 x 3) (sqrt.f64 2))))))))))))) (fma.f64 4 (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (fma.f64 2 (/.f64 (/.f64 (.f64 l l) t) (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))) (fma.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (.f64 x x))) (fma.f64 2 (/.f64 t (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (*.f64 4 (/.f64 (/.f64 t (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))))))))))
	39.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	59.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	58.9b	(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)))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (neg.f64 (sqrt.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (*.f64 x x))))))))

Compiler

Compiled 21631 to 14597 computations (32.5% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(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))))))))
✓	10.1b	(.f64 (.f64 l l) (pow.f64 x -3))
✓	19.7b	(.f64 (.f64 t t) (pow.f64 x -3))
✓	28.1b	(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))))))))))

series463.0ms (2.7%)

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
44.0ms	(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
40.0ms	(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
32.0ms	(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

rewrite44.0ms (0.3%)

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

simplify136.0ms (0.8%)

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

prune400.0ms (2.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	144	13	157

Error

0.4b

Counts

157 → 13

Alt Table

Status	Error	Program
	54.9b	(/.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)))))))
	56.6b	(/.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))
	40.2b	(/.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)))
	35.3b	(/.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 (sqrt.f64 2) (.f64 x t)) l)))))
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
▶	33.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (pow.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)))))))))) 2) 1/2) (pow.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)))))))))) 1/2)))
	39.3b	(/.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))))))))
	55.1b	(/.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))))))))))
	42.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (fma.f64 2 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (fma.f64 2 (/.f64 (.f64 t t) (+.f64 x -1)) (+.f64 (/.f64 (.f64 l l) (/.f64 (+.f64 x -1) x)) (/.f64 (.f64 l l) (+.f64 x -1))))) (.f64 l l))))
	47.3b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (+.f64 (/.f64 (.f64 l l) (.f64 (.f64 t (sqrt.f64 2)) (.f64 x x))) (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (sqrt.f64 2)))) (fma.f64 3 (/.f64 (/.f64 (pow.f64 l 4) (pow.f64 t 3)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 4 (/.f64 t (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (fma.f64 6 (/.f64 (.f64 l l) (.f64 (.f64 t (pow.f64 (sqrt.f64 2) 5)) (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 (.f64 l l) t) (.f64 x (sqrt.f64 2))) (fma.f64 1/2 (/.f64 (/.f64 (pow.f64 l 6) (pow.f64 t 5)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 t (sqrt.f64 2) (.f64 2 (+.f64 (/.f64 t (.f64 (.f64 x x) (sqrt.f64 2))) (/.f64 t (.f64 (pow.f64 x 3) (sqrt.f64 2))))))))))))) (fma.f64 4 (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (fma.f64 2 (/.f64 (/.f64 (.f64 l l) t) (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))) (fma.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (.f64 x x))) (fma.f64 2 (/.f64 t (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (*.f64 4 (/.f64 (/.f64 t (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))))))))))
	39.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	59.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	58.9b	(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)))))

Compiler

Compiled 21478 to 15200 computations (29.2% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	10.1b	(.f64 (.f64 l l) (pow.f64 x -3))
✓	13.1b	(pow.f64 (pow.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)))))))))) 2) 1/2)
	19.7b	(.f64 (.f64 t t) (pow.f64 x -3))
✓	28.9b	(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))))))))))

series2.0s (11.9%)

Counts

2 → 72

Calls

18 calls:

288.0ms	(pow.f64 (pow.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)))))))))) 2) 1/2)	l	-inf
283.0ms	(pow.f64 (pow.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)))))))))) 2) 1/2)	l	inf
230.0ms	(pow.f64 (pow.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)))))))))) 2) 1/2)	t	-inf
228.0ms	(pow.f64 (pow.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)))))))))) 2) 1/2)	t	inf
217.0ms	(pow.f64 (pow.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)))))))))) 2) 1/2)	t	0

rewrite42.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

287×	`log1p-expm1-u_binary64`
287×	`expm1-log1p-u_binary64`
280×	`add-cube-cbrt_binary64`
280×	`add-cbrt-cube_binary64`
280×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	144
1	648	144

Stop Event

1×	node limit

Counts

2 → 41

simplify299.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

462×	`*-commutative_binary64`
411×	`+-commutative_binary64`
383×	`fma-def_binary64`
356×	`associate-+r+_binary64`
245×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1242	44714

Stop Event

1×	node limit

Counts

113 → 112

prune2.1s (12.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	252	3	255
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	253	15	268

Error

0.4b

Counts

268 → 15

Alt Table

Status	Error	Program
	54.9b	(/.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)))))))
	56.6b	(/.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))
	33.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (fma.f64 4 (.f64 (.f64 t t) (pow.f64 x -3)) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (fma.f64 2 (.f64 (pow.f64 x -3) (.f64 l l)) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x)))))))))) (pow.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)))))))))) 1/2)))
	40.2b	(/.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)))
	35.3b	(/.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 (sqrt.f64 2) (.f64 x t)) l)))))
	47.3b	(/.f64 (.f64 (sqrt.f64 2) t) (-.f64 (+.f64 (+.f64 (/.f64 (.f64 l l) (.f64 (.f64 t (sqrt.f64 2)) (.f64 x x))) (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (sqrt.f64 2)))) (fma.f64 3 (/.f64 (/.f64 (pow.f64 l 4) (pow.f64 t 3)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 4 (/.f64 t (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (fma.f64 6 (/.f64 (.f64 l l) (.f64 (.f64 t (pow.f64 (sqrt.f64 2) 5)) (pow.f64 x 3))) (+.f64 (/.f64 (/.f64 (.f64 l l) t) (.f64 x (sqrt.f64 2))) (fma.f64 1/2 (/.f64 (/.f64 (pow.f64 l 6) (pow.f64 t 5)) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 5))) (fma.f64 t (sqrt.f64 2) (.f64 2 (+.f64 (/.f64 t (.f64 (.f64 x x) (sqrt.f64 2))) (/.f64 t (.f64 (pow.f64 x 3) (sqrt.f64 2))))))))))))) (fma.f64 4 (/.f64 (/.f64 (.f64 l l) t) (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 2) 3))) (fma.f64 2 (/.f64 (/.f64 (.f64 l l) t) (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (+.f64 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))) (fma.f64 1/2 (/.f64 (pow.f64 l 4) (.f64 (.f64 (pow.f64 t 3) (pow.f64 (sqrt.f64 2) 3)) (.f64 x x))) (fma.f64 2 (/.f64 t (.f64 (.f64 x x) (pow.f64 (sqrt.f64 2) 3))) (*.f64 4 (/.f64 (/.f64 t (pow.f64 (sqrt.f64 2) 3)) (pow.f64 x 3))))))))))
	59.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (pow.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)))))))))) 2) 1/2) (pow.f64 (pow.f64 (exp.f64 1/3) (+.f64 (log.f64 (+.f64 (/.f64 2 x) (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (.f64 x x))))) (*.f64 -2 (log.f64 (/.f64 -1 l))))) 1/2)))
	39.3b	(/.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))))))))
	55.1b	(/.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))))))))))
	42.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (fma.f64 2 (/.f64 (.f64 t t) (/.f64 (+.f64 x -1) x)) (fma.f64 2 (/.f64 (.f64 t t) (+.f64 x -1)) (+.f64 (/.f64 (.f64 l l) (/.f64 (+.f64 x -1) x)) (/.f64 (.f64 l l) (+.f64 x -1))))) (.f64 l l))))
	39.6b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1))))))))
	38.4b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (+.f64 x -1)) (.f64 2 (/.f64 x (+.f64 x -1)))))))
	59.0b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 1 (+.f64 x -1)) (-.f64 (/.f64 x (+.f64 x -1)) 1)))))
	55.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (pow.f64 (pow.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)))))))))) 2) 1/2) (pow.f64 (pow.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 2))) (+.f64 (.f64 2 (/.f64 (pow.f64 l 2) (pow.f64 x 3))) (.f64 2 (/.f64 (pow.f64 l 2) x)))) 1/3) 1/2)))
	58.9b	(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)))))

Compiler

Compiled 107526 to 78269 computations (27.2% saved)

regimes2.9s (17%)

Accuracy

Total 10.9b remaining (97.3%)

Threshold costs 0b (0%)

Counts

148 → 5

Compiler

Compiled 51478 to 33515 computations (34.9% saved)

bsearch515.0ms (3%)

Algorithm

4×	binary-search

Calls

4 calls:

145.0ms	t
137.0ms	t
136.0ms	t
85.0ms	t

Steps

Iters	Point		Range
3.236051765993995e+46	∈ [	6.094670298516006e+33	,	4.043502652412787e+46	]
1.0811679065075598e-170	∈ [	4.6785219673180447e-172	,	1.0957728150550299e-170	]
-1.279046527317441e-150	∈ [	-1.3127158984844458e-150	,	-9.743583574454096e-153	]
-2.318016481841386e+76	∈ [	-2.154207838409582e+78	,	-1.1307024253363977e+76	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`*-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	68	259
1	85	259
2	94	259
3	99	259
4	101	259

Stop Event

1×

saturated

end622.0ms (3.7%)

Stop Event

1×

fuel

Compiler

Compiled 1300 to 890 computations (31.5% saved)

Details

analyze1.1s (6.6%)

sample3.2s (18.6%)

preprocess45.0ms (0.3%)

simplify25.0ms (0.1%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series882.0ms (5.2%)

rewrite49.0ms (0.3%)

simplify206.0ms (1.2%)

prune833.0ms (4.9%)

localize26.0ms (0.2%)

series385.0ms (2.3%)

rewrite41.0ms (0.2%)

simplify128.0ms (0.8%)

prune423.0ms (2.5%)

localize34.0ms (0.2%)

series463.0ms (2.7%)

rewrite44.0ms (0.3%)

simplify136.0ms (0.8%)

prune400.0ms (2.4%)

localize38.0ms (0.2%)

series2.0s (11.9%)

rewrite42.0ms (0.2%)

simplify299.0ms (1.8%)

prune2.1s (12.6%)

regimes2.9s (17%)

bsearch515.0ms (3%)

simplify7.0ms (0%)

end622.0ms (3.7%)

Profiling