Details

analyze1.1s (6.7%)

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)

sample3.3s (20.1%)

Results

928.0ms	5458×	body	128	valid
750.0ms	1268×	body	1024	valid
453.0ms	792×	body	1024	invalid
371.0ms	883×	body	512	valid
250.0ms	1586×	body	128	invalid
218.0ms	504×	body	512	invalid
167.0ms	571×	body	256	valid
69.0ms	261×	body	256	invalid
51.0ms	76×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

667×	`fma-def_binary64`
506×	`fma-neg_binary64`
500×	`distribute-rgt-in_binary64`
420×	`distribute-lft-in_binary64`
403×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	48	39
2	103	39
3	222	39
4	455	39
5	975	39
6	2136	39
7	4390	39
8	4971	39

prune3.0ms (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

46.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	46.8b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))

Compiler

Compiled 114 to 72 computations (36.8% 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 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
✓	0.4b	(*.f64 (sqrt.f64 2) t)
✓	16.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	22.0b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series1.1s (6.3%)

Counts

4 → 120

Calls

4 calls:

796.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
189.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
62.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
3.0ms	(*.f64 (sqrt.f64 2) t)

rewrite94.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

432×	`prod-diff_binary64`
193×	`add-sqr-sqrt_binary64`
186×	`log1p-expm1-u_binary64`
186×	`expm1-log1p-u_binary64`
183×	`add-log-exp_binary64`

Counts

4 → 148

Calls

4 calls:

89.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))
89.0ms	(*.f64 (sqrt.f64 2) t)
89.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
89.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	105
1	397	105
2	4687	105
3	5518	105

simplify257.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

268 → 304

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28688
1	5075	28688

prune817.0ms (4.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	296	8	304
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	297	8	305

Error

6.6b

Counts

305 → 8

Alt Table

Status	Error	Program
▶	34.5b	(/.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))))))))
	36.9b	(/.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))))))
	38.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 2)))
	63.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (-.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) 1)) l))
	39.0b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
	40.8b	(/.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) (sqrt.f64 (.f64 (.f64 t t) (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
	54.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 t t))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))))

Compiler

Compiled 43529 to 31927 computations (26.7% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.4b	(/.f64 (*.f64 t t) x)
✓	17.4b	(/.f64 (.f64 l l) (.f64 x x))
✓	20.4b	(/.f64 (.f64 t t) (.f64 x x))
✓	28.5b	(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)))))))

series221.0ms (1.3%)

Counts

4 → 108

Calls

4 calls:

153.0ms	(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)))))))
33.0ms	(/.f64 (.f64 t t) (.f64 x x))
26.0ms	(/.f64 (.f64 l l) (.f64 x x))
9.0ms	(/.f64 (*.f64 t t) x)

rewrite75.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

306×	`prod-diff_binary64`
206×	`add-sqr-sqrt_binary64`
198×	`log1p-expm1-u_binary64`
198×	`expm1-log1p-u_binary64`
196×	`add-log-exp_binary64`

Counts

4 → 123

Calls

4 calls:

73.0ms	(/.f64 (*.f64 t t) x)
73.0ms	(/.f64 (.f64 l l) (.f64 x x))
73.0ms	(/.f64 (.f64 t t) (.f64 x x))
73.0ms	(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)))))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	81
1	425	67
2	4793	67
3	5333	67

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

231 → 191

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	417	7585
1	1334	6486
2	5292	6486

prune291.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	185	6	191
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	189	10	199

Error

0.4b

Counts

199 → 10

Alt Table

Status	Error	Program
	53.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	34.5b	(/.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))))))))
	52.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
▶	31.9b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))))) 1/4) 2))
	38.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 2)))
	32.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	40.9b	(/.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)))))))
	54.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 t t))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))))

Compiler

Compiled 15364 to 9255 computations (39.8% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.2b	(fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))
✓	8.5b	(/.f64 (*.f64 l l) x)
	10.4b	(/.f64 (*.f64 t t) x)
✓	29.3b	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))) 1/4)

series323.0ms (1.9%)

Counts

3 → 96

Calls

3 calls:

263.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))) 1/4)

50.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))

9.0ms

(/.f64 (*.f64 l l) x)

rewrite72.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

215×	`prod-diff_binary64`
208×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
198×	`add-log-exp_binary64`

Counts

3 → 68

Calls

3 calls:

71.0ms

(fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))

71.0ms

(/.f64 (*.f64 l l) x)

71.0ms

(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (*.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (/.f64 (*.f64 l l) x)))))) 1/4)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	88
1	448	86
2	4681	86
3	5112	86

simplify142.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

598×	`times-frac_binary64`
583×	`associate-/r*_binary64`
576×	`fma-def_binary64`
447×	`associate-/l*_binary64`
232×	`*-commutative_binary64`

Counts

164 → 153

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	585	11205
1	1972	10433
2	5442	10433

prune410.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	178	3	181
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	180	11	191

Error

0.3b

Counts

191 → 11

Alt Table

Status	Error	Program
	53.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	34.5b	(/.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))))))))
	52.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (*.f64 2 (fma.f64 t t (pow.f64 (/.f64 l (sqrt.f64 x)) 2)))))) 1/4) 2))
▶	28.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8)) 2))
	38.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 2)))
	32.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	55.9b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (*.f64 (log.f64 l) 2))) 2))
	54.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 t t))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))))

Compiler

Compiled 19634 to 13694 computations (30.3% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(pow.f64 (.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8)) 2)
✓	0.5b	(.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8))
✓	4.2b	(fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))
✓	29.4b	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8)

series1.0s (6.2%)

Counts

4 → 144

Calls

4 calls:

426.0ms	(pow.f64 (.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8)) 2)
269.0ms	(.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8))
266.0ms	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8)
70.0ms	(fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))

rewrite75.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

372×	`log1p-udef_binary64`
213×	`add-sqr-sqrt_binary64`
212×	`log1p-expm1-u_binary64`
212×	`expm1-log1p-u_binary64`
205×	`add-log-exp_binary64`

Counts

4 → 73

Calls

4 calls:

73.0ms	(pow.f64 (.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8)) 2)
73.0ms	(.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8))
73.0ms	(fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))
73.0ms	(pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (*.f64 l (/.f64 l x))))))) 1/8)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	174
1	462	162
2	4586	162
3	5346	162

simplify473.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

519×	`*-commutative_binary64`
375×	`+-commutative_binary64`
306×	`fma-def_binary64`
274×	`associate-+r+_binary64`
190×	`associate-*r/_binary64`

Counts

217 → 282

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1339	30878
1	4879	30878
2	4992	30878
3	4970	30878

prune1.3s (7.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	398	2	400
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	399	12	411

Error

0.2b

Counts

411 → 12

Alt Table

Status	Error	Program
	53.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
✓	34.5b	(/.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))))))))
	52.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
	40.4b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (*.f64 2 (pow.f64 (hypot.f64 (/.f64 l x) (hypot.f64 t (/.f64 l (sqrt.f64 x)))) 2))))))
✓	28.1b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (.f64 (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8) (pow.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (.f64 t (/.f64 t x)) (.f64 2 (+.f64 (pow.f64 (/.f64 l x) 2) (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/8)) 2))
	38.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 2)))
	40.4b	(/.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 t x)) (*.f64 2 (pow.f64 (hypot.f64 (/.f64 l x) (hypot.f64 t (/.f64 l (sqrt.f64 x)))) 2)))) 1/4) 2))
	32.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 4 (pow.f64 (/.f64 t x) 2) (fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x))))))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x))))))))
	38.7b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	55.9b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (exp.f64 1/4) (+.f64 (log.f64 (+.f64 (/.f64 2 x) (/.f64 2 (.f64 x x)))) (*.f64 (log.f64 l) 2))) 2))
	54.8b	(/.f64 (sqrt.f64 (.f64 2 (.f64 t t))) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))))

Compiler

Compiled 70725 to 48899 computations (30.9% saved)

regimes4.3s (26.1%)

Accuracy

Total 8.3b remaining (92.5%)

Threshold costs 0b (0%)

Counts

194 → 5

Compiler

Compiled 56855 to 38783 computations (31.8% saved)

bsearch671.0ms (4%)

Steps

Iters	Range		Point
7	2.650672706922735e+25	1.0695129777473211e+27	1.0565592753655027e+27
11	2.6983253666016455e-191	5.218332026261204e-168	2.7248008057053303e-191
10	-5.440220649842031e-302	2.1845940057302437e-303	2.1563523231601638e-303
10	-2.894312660477816e+148	-2.176424090353494e+137	-9.637691388536258e+147

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
10×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	251
1	98	251
2	107	251
3	112	251
4	114	251
5	112	251

end316.0ms (1.9%)

Compiler: Compiled 771 to 509 computations (34% saved)

Details

analyze1.1s (6.7%)

sample3.3s (20.1%)

simplify50.0ms (0.3%)

prune3.0ms (0%)

localize16.0ms (0.1%)

series1.1s (6.3%)

rewrite94.0ms (0.6%)

simplify257.0ms (1.5%)

prune817.0ms (4.9%)

localize21.0ms (0.1%)

series221.0ms (1.3%)

rewrite75.0ms (0.5%)

simplify103.0ms (0.6%)

prune291.0ms (1.8%)

localize25.0ms (0.1%)

series323.0ms (1.9%)

rewrite72.0ms (0.4%)

simplify142.0ms (0.9%)

prune410.0ms (2.5%)

localize25.0ms (0.1%)

series1.0s (6.2%)

rewrite75.0ms (0.5%)

simplify473.0ms (2.8%)

prune1.3s (7.6%)

regimes4.3s (26.1%)

bsearch671.0ms (4%)

simplify8.0ms (0%)

end316.0ms (1.9%)

Profiling