Details

analyze1.3s (8.9%)

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)

sample3.5s (24.3%)

Results

979.0ms	5453×	body	128	valid
706.0ms	1224×	body	1024	valid
545.0ms	858×	body	1024	invalid
400.0ms	941×	body	512	valid
256.0ms	1608×	body	128	invalid
207.0ms	510×	body	512	invalid
174.0ms	566×	body	256	valid
91.0ms	314×	body	256	invalid
53.0ms	72×	body	2048	valid

Compiler

Compiled 92 to 62 computations (32.6% saved)

simplify59.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

422×	`rules-49-rev_binary64`
389×	`rules-4_binary64`
299×	`rules-24-rev_binary64`
201×	`rules-33_binary64`
158×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	39
1	49	39
2	133	39
3	486	39
4	3207	39
5	4864	39
6	5524	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

43.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	43.4b	(/.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)

localize14.0ms (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)
✓	11.9b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
✓	20.5b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))

series1.0s (7.3%)

Counts

4 → 120

Calls

4 calls:

774.0ms	(/.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))))
197.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)))
70.0ms	(-.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)

rewrite109.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

470×	`prod-diff_binary64`
188×	`egg-rr`
180×	`add-sqr-sqrt_binary64`
173×	`log1p-expm1-u_binary64`
173×	`expm1-log1p-u_binary64`

Counts

4 → 188

Calls

4 calls:

103.0ms	(/.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))))
103.0ms	(*.f64 (sqrt.f64 2) t)
103.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l))
103.0ms	(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	429	105
2	4790	105
3	5614	105
0	0	0
1	0	0

simplify265.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

632×	`rules-20_binary64`
409×	`rules-21_binary64`
385×	`fma-def_binary64`
336×	`rules-2_binary64`
225×	`rules-5-rev_binary64`

Counts

308 → 345

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1507	28633
1	5053	28633

prune1.6s (10.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	335	10	345
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	336	10	346

Error

4.8b

Counts

346 → 10

Alt Table

Status	Error	Program
	41.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (-.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l) (+.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l))))
	42.8b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (+.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (.f64 l l)) (fma.f64 (neg.f64 l) l (.f64 l l)))))
	43.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	41.2b	(/.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))))))
	36.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) -1))
	40.6b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1)))))))
▶	29.8b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (*.f64 t t))))))
	47.2b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	43.5b	(.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
	36.7b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))

Compiler

Compiled 45494 to 33065 computations (27.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))
✓	7.4b	(/.f64 (*.f64 l l) x)
✓	9.0b	(/.f64 (*.f64 t t) x)
✓	25.6b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))

series141.0ms (1%)

Counts

4 → 116

Calls

4 calls:

80.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))
40.0ms	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))
10.0ms	(/.f64 (*.f64 t t) x)
10.0ms	(/.f64 (*.f64 l l) x)

rewrite93.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

640×	`prod-diff_binary64`
153×	`egg-rr`
141×	`add-sqr-sqrt_binary64`
137×	`log1p-expm1-u_binary64`
137×	`expm1-log1p-u_binary64`

Counts

4 → 153

Calls

4 calls:

88.0ms	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t))))
88.0ms	(/.f64 (*.f64 l l) x)
88.0ms	(/.f64 (*.f64 t t) x)
88.0ms	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (.f64 t t)))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	68
1	336	64
2	4101	64
3	5255	64
0	0	0
1	0	0

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary64`
483×	`rules-21_binary64`
381×	`rules-15-rev_binary64`
293×	`fma-def_binary64`
214×	`rules-13_binary64`

Counts

269 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	187	3980
1	634	3555
2	3150	3555
3	5425	3555

prune235.0ms (1.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	208	7	215
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	212	13	225

Error

0.4b

Counts

225 → 13

Alt Table

Status	Error	Program
	41.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (-.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l) (+.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l))))
	37.7b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))) 3/2)))
	47.2b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x)))))
	36.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) -1))
	40.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (pow.f64 (/.f64 l (sqrt.f64 x)) 2) (.f64 t t))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)))))
▶	26.7b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (*.f64 t t))))))
	29.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))) 1/4) 2))
	43.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	43.5b	(.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)) (.f64 (/.f64 (.f64 t t) (.f64 l (sqrt.f64 2))) (+.f64 (sqrt.f64 x) (.f64 2 (sqrt.f64 (/.f64 1 x)))))))
	36.7b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))

Compiler

Compiled 9716 to 5331 computations (45.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(+.f64 (.f64 l (/.f64 l x)) (.f64 t t))
✓	3.8b	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (.f64 t t))))
	9.0b	(/.f64 (*.f64 t t) x)
✓	25.6b	(sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (+.f64 (.f64 l (/.f64 l x)) (.f64 t t)))))

series133.0ms (0.9%)

Counts

3 → 104

Calls

3 calls:

79.0ms

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

37.0ms

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

16.0ms

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

rewrite95.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

726×	`prod-diff_binary64`
143×	`egg-rr`
143×	`add-sqr-sqrt_binary64`
138×	`log1p-expm1-u_binary64`
138×	`expm1-log1p-u_binary64`

Counts

3 → 143

Calls

3 calls:

91.0ms

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

91.0ms

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

91.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	61
1	338	61
2	4251	61
3	5596	61
0	0	0
1	0	0

simplify92.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

836×	`fma-neg_binary64`
484×	`rules-21_binary64`
381×	`rules-15-rev_binary64`
294×	`fma-def_binary64`
214×	`rules-13_binary64`

Counts

247 → 207

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	188	4043
1	635	3564
2	3154	3564
3	5429	3564

prune275.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	240	13	253

Error

0.4b

Counts

253 → 13

Alt Table

Status	Error	Program
	47.2b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x)))))
	40.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (*.f64 2 (pow.f64 (hypot.f64 t (/.f64 l (sqrt.f64 x))) 2)))))
	43.5b	(.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
	36.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) -1))
▶	26.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x)))))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x)))))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)))))
	36.8b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x))))) 3/2)))
	41.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (-.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l) (+.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l))))
	29.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))) 1/4) 2))
	43.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)) (.f64 (/.f64 (.f64 t t) (.f64 l (sqrt.f64 2))) (+.f64 (sqrt.f64 x) (.f64 2 (sqrt.f64 (/.f64 1 x)))))))
	36.7b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))

Compiler

Compiled 10548 to 5675 computations (46.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.8b	(fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (*.f64 l (/.f64 l x)))))
	9.0b	(/.f64 (*.f64 t t) x)
✓	12.0b	(sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (*.f64 l (/.f64 l x)))))) 2))
✓	26.4b	(cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (*.f64 l (/.f64 l x))))))

series254.0ms (1.8%)

Counts

3 → 108

Calls

3 calls:

109.0ms

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

105.0ms

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

38.0ms

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

rewrite91.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

408×	`prod-diff_binary64`
249×	`log1p-udef_binary64`
143×	`add-sqr-sqrt_binary64`
136×	`log1p-expm1-u_binary64`
136×	`expm1-log1p-u_binary64`

Counts

3 → 127

Calls

3 calls:

86.0ms

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

86.0ms

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

86.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	76
1	348	76
2	4052	76
3	5209	76
0	0	0
1	0	0

simplify131.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

475×	`fma-def_binary64`
369×	`rules-20_binary64`
347×	`rules-13_binary64`
284×	`rules-4_binary64`
205×	`rules-21_binary64`

Counts

235 → 167

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	339	9376
1	1245	8971
2	5135	8971

prune562.0ms (3.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	398	1	399
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	398	14	412

Error

0.4b

Counts

412 → 14

Alt Table

Status	Error	Program
	47.2b	(.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (/.f64 1 (.f64 2 (+.f64 (/.f64 (.f64 (.f64 t t) x) (-.f64 x 1)) (/.f64 (.f64 t t) (-.f64 x 1)))))))
	40.8b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 t (sqrt.f64 (+.f64 2 (/.f64 4 x)))))
	40.1b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (*.f64 2 (pow.f64 (hypot.f64 t (/.f64 l (sqrt.f64 x))) 2)))))
	43.5b	(.f64 (sqrt.f64 2) (/.f64 t (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l)))))
	36.4b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (.f64 t (sqrt.f64 (+.f64 (/.f64 2 (-.f64 x 1)) (.f64 2 (/.f64 x (-.f64 x 1)))))) -1))
✓	26.9b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x)))))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x)))))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (neg.f64 (.f64 (*.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)))))
	36.8b	(/.f64 (.f64 (sqrt.f64 2) t) (cbrt.f64 (pow.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x))))) 3/2)))
	27.1b	(/.f64 (.f64 (sqrt.f64 2) t) (.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x)))))) 2)) (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (.f64 l (/.f64 l x))))))) 3))))
	41.3b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (.f64 (-.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l) (+.f64 (sqrt.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l)))) l))))
	29.8b	(/.f64 (.f64 (sqrt.f64 2) t) (pow.f64 (pow.f64 (fma.f64 4 (/.f64 (.f64 t t) x) (.f64 2 (fma.f64 t t (/.f64 (.f64 l l) x)))) 1/4) 2))
	43.4b	(log1p.f64 (expm1.f64 (/.f64 (.f64 t (sqrt.f64 2)) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (fma.f64 2 (.f64 t t) (.f64 l l))) (*.f64 l l))))))
	55.1b	(/.f64 (.f64 (sqrt.f64 2) t) (fma.f64 (.f64 l (sqrt.f64 2)) (sqrt.f64 (/.f64 1 x)) (.f64 (/.f64 (.f64 t t) (.f64 l (sqrt.f64 2))) (+.f64 (sqrt.f64 x) (.f64 2 (sqrt.f64 (/.f64 1 x)))))))
	36.7b	(.f64 -1 (.f64 (sqrt.f64 2) (sqrt.f64 (/.f64 1 (+.f64 (/.f64 2 (-.f64 x 1)) (*.f64 2 (/.f64 x (-.f64 x 1))))))))

Compiler

Compiled 31251 to 17268 computations (44.7% saved)

regimes3.6s (25%)

Accuracy

Total 8.2b remaining (91.1%)

Threshold costs 0b (0%)

Counts

224 → 5

Compiler

Compiled 44942 to 30445 computations (32.3% saved)

bsearch407.0ms (2.8%)

Steps

Iters	Range		Point
4	1.5288617482539403e+75	2.4106105061322775e+75	2.3742936810086067e+75
7	1.1750608672426329e-148	8.413816716285449e-147	1.1939357900903373e-148
7	1.3635884033584413e-220	5.270116407780659e-219	5.2112458239765657e-219
6	-3.5890833092905013e+140	-3.7674290287367425e+139	-3.048430524696057e+140

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	202
1	60	202
2	59	202

end298.0ms (2.1%)

Compiler: Compiled 715 to 494 computations (30.9% saved)

Details

analyze1.3s (8.9%)

sample3.5s (24.3%)

simplify59.0ms (0.4%)

prune3.0ms (0%)

localize14.0ms (0.1%)

series1.0s (7.3%)

rewrite109.0ms (0.8%)

simplify265.0ms (1.8%)

prune1.6s (10.8%)

localize14.0ms (0.1%)

series141.0ms (1%)

rewrite93.0ms (0.6%)

simplify92.0ms (0.6%)

prune235.0ms (1.6%)

localize14.0ms (0.1%)

series133.0ms (0.9%)

rewrite95.0ms (0.7%)

simplify92.0ms (0.6%)

prune275.0ms (1.9%)

localize19.0ms (0.1%)

series254.0ms (1.8%)

rewrite91.0ms (0.6%)

simplify131.0ms (0.9%)

prune562.0ms (3.9%)

regimes3.6s (25%)

bsearch407.0ms (2.8%)

simplify3.0ms (0%)

end298.0ms (2.1%)

Profiling