Details

analyze1.0s (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)

sample3.0s (23.2%)

Results

847.0ms	5476×	body	128	valid
591.0ms	1168×	body	1024	valid
435.0ms	866×	body	1024	invalid
372.0ms	955×	body	512	valid
228.0ms	1578×	body	128	invalid
182.0ms	492×	body	512	invalid
148.0ms	573×	body	256	valid
81.0ms	300×	body	256	invalid
56.0ms	84×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify50.0ms (0.4%)

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

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

42.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.6b	(/.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))))
✓	0.5b	(*.f64 (sqrt.f64 2) t)
✓	9.4b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	23.9b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series1.7s (13.2%)

Counts

4 → 120

Calls

4 calls:

1.4s	(/.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))))
286.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
71.0ms	(-.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)

rewrite100.0ms (0.8%)

Algorithm

2×	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 → 144

Calls

4 calls:

95.0ms	(/.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))))
95.0ms	(*.f64 (sqrt.f64 2) t)
95.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
95.0ms	(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
0	0	0
1	0	0

simplify244.0ms (1.9%)

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

264 → 301

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28688
1	5075	28688

prune779.0ms (6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	293	8	301
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	294	8	302

Error

3.1b

Counts

302 → 8

Alt Table

Status	Error	Program
▶	31.7b	(/.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 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	62.6b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2))))
	35.4b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	63.6b	(neg.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (-.f64 x 1))) -1))) (/.f64 (.f64 t (sqrt.f64 2)) l)))
	39.5b	(/.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))))))))
	39.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	35.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
	35.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))

Compiler

Compiled 43469 to 31911 computations (26.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	10.1b	(/.f64 (*.f64 t t) x)
✓	10.7b	(/.f64 (.f64 l l) (.f64 x x))
✓	18.0b	(/.f64 (.f64 t t) (.f64 x x))
✓	27.0b	(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)))))))

series298.0ms (2.3%)

Counts

4 → 108

Calls

4 calls:

230.0ms	(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)))))))
29.0ms	(/.f64 (.f64 l l) (.f64 x x))
29.0ms	(/.f64 (.f64 t t) (.f64 x x))
10.0ms	(/.f64 (*.f64 t t) x)

rewrite77.0ms (0.6%)

Algorithm

2×	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 → 121

Calls

4 calls:

74.0ms	(/.f64 (*.f64 t t) x)
74.0ms	(/.f64 (.f64 l l) (.f64 x x))
74.0ms	(/.f64 (.f64 t t) (.f64 x x))
74.0ms	(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: 0 (0.0ms)

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

simplify100.0ms (0.8%)

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

229 → 190

Iterations

Useful iterations: 1 (0.0ms)

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

prune300.0ms (2.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	182	8	190
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	184	14	198

Error

0.1b

Counts

198 → 14

Alt Table

Status	Error	Program
	35.4b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	56.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	31.1b	(/.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))))))))))
	39.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	35.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	35.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
✓	31.7b	(/.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 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	62.6b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2))))
	56.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
▶	30.9b	(/.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))
	41.3b	(/.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)))))) 3/2) 1/3))
	40.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 x (.f64 x t))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
	39.5b	(/.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))))))))
	31.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.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))))))) (cbrt.f64 (sqrt.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))))))))))

Compiler

Compiled 15749 to 9528 computations (39.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.6b	(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)))))
✓	5.8b	(/.f64 (*.f64 l l) x)
	10.1b	(/.f64 (*.f64 t t) x)
✓	27.7b	(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)

series545.0ms (4.2%)

Counts

3 → 96

Calls

3 calls:

477.0ms

(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)

56.0ms

(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)))))

11.0ms

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

rewrite73.0ms (0.6%)

Algorithm

2×	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 → 66

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: 0 (0.0ms)

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

simplify143.0ms (1.1%)

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

162 → 151

Iterations

Useful iterations: 1 (0.0ms)

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

prune401.0ms (3.1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	177	2	179
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	178	15	193

Error

0.0b

Counts

193 → 15

Alt Table

Status	Error	Program
	35.4b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	56.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	31.1b	(/.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))))))))))
	39.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	35.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	35.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
✓	31.7b	(/.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 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	62.6b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2))))
	56.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
▶	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 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/4) 2))
	41.3b	(/.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)))))) 3/2) 1/3))
	40.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 x (.f64 x t))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
	39.5b	(/.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))))))))
	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 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (.f64 l (/.f64 l x))) 3)))))) 1/4) 2))
	31.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.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))))))) (cbrt.f64 (sqrt.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))))))))))

Compiler

Compiled 19914 to 13916 computations (30.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(fma.f64 t t (*.f64 l (/.f64 l x)))
✓	3.6b	(fma.f64 4 (/.f64 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (*.f64 l (/.f64 l x))))))
	10.1b	(/.f64 (*.f64 t t) x)
✓	27.7b	(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 l (/.f64 l x))))))) 1/4)

series563.0ms (4.3%)

Counts

3 → 108

Calls

3 calls:

488.0ms

(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 l (/.f64 l x))))))) 1/4)

58.0ms

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

16.0ms

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

rewrite87.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

536×	`prod-diff_binary64`
198×	`add-sqr-sqrt_binary64`
192×	`log1p-expm1-u_binary64`
192×	`expm1-log1p-u_binary64`
188×	`add-log-exp_binary64`

Counts

3 → 58

Calls

3 calls:

85.0ms

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

85.0ms

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

84.0ms

(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 l (/.f64 l x))))))) 1/4)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	92
1	425	90
2	4833	90
3	5931	90
0	0	0
1	0	0

simplify143.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

166 → 147

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	586	11436
1	1973	10558
2	5442	10558

prune358.0ms (2.7%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	175	15	190

Error

0.0b

Counts

190 → 15

Alt Table

Status	Error	Program
	35.4b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 t (sqrt.f64 2) (fma.f64 2 (/.f64 t (.f64 x (sqrt.f64 2))) (/.f64 (.f64 l l) (.f64 t (*.f64 x (sqrt.f64 2)))))))
	56.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x))))))
	31.1b	(/.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))))))))))
	39.9b	(neg.f64 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1))))))))
	35.3b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (*.f64 x x)))))))
	35.5b	(.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))))
✓	31.7b	(/.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 2 (/.f64 (.f64 l l) (.f64 x x)) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))))
	62.6b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (+.f64 (/.f64 (.f64 (pow.f64 l 2) x) (-.f64 x 1)) (/.f64 (pow.f64 l 2) (-.f64 x 1))) (pow.f64 l 2))))
	56.7b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 l (sqrt.f64 (+.f64 (/.f64 2 x) (/.f64 2 (*.f64 x x)))))))
✓	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 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x))))))) 1/4) 2))
	41.3b	(/.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)))))) 3/2) 1/3))
	40.6b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 1 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))) (+.f64 (/.f64 (.f64 l l) (.f64 x t)) (/.f64 (.f64 l l) (.f64 x (.f64 x t))))) (.f64 t (sqrt.f64 (+.f64 2 (+.f64 (/.f64 4 x) (/.f64 4 (.f64 x x)))))))))
	39.5b	(/.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))))))))
	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 (.f64 t t) x) (fma.f64 2 (pow.f64 (/.f64 l x) 2) (.f64 2 (fma.f64 t t (pow.f64 (cbrt.f64 (.f64 l (/.f64 l x))) 3)))))) 1/4) 2))
	31.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.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))))))) (cbrt.f64 (sqrt.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))))))))))

Compiler

Compiled 19259 to 13433 computations (30.3% saved)

regimes1.9s (14.8%)

Accuracy

Total 8.4b remaining (96%)

Threshold costs 0b (0%)

Counts

102 → 5

Compiler

Compiled 25017 to 18053 computations (27.8% saved)

bsearch584.0ms (4.5%)

Steps

Iters	Range		Point
9	1.8613556924582604e+102	3.473746701143527e+108	1.041564456713424e+103
8	2.9956561137468985e-181	1.569773600611297e-178	3.0381553065904004e-181
12	-1.3351201806537359e-275	3.0908814134634187e-298	3.0571751654539254e-298
9	-9.094742420489952e+51	-1.0338840644233167e+46	-8.979527677928165e+51

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
7×	`+-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	63	244
1	85	244
2	94	244
3	99	244
4	101	244
5	99	244

end369.0ms (2.8%)

Compiler: Compiled 911 to 612 computations (32.8% saved)

Details

analyze1.0s (8%)

sample3.0s (23.2%)

simplify50.0ms (0.4%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series1.7s (13.2%)

rewrite100.0ms (0.8%)

simplify244.0ms (1.9%)

prune779.0ms (6%)

localize21.0ms (0.2%)

series298.0ms (2.3%)

rewrite77.0ms (0.6%)

simplify100.0ms (0.8%)

prune300.0ms (2.3%)

localize26.0ms (0.2%)

series545.0ms (4.2%)

rewrite73.0ms (0.6%)

simplify143.0ms (1.1%)

prune401.0ms (3.1%)

localize24.0ms (0.2%)

series563.0ms (4.3%)

rewrite87.0ms (0.7%)

simplify143.0ms (1.1%)

prune358.0ms (2.7%)

regimes1.9s (14.8%)

bsearch584.0ms (4.5%)

simplify7.0ms (0.1%)

end369.0ms (2.8%)

Profiling