Details

analyze392.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

Compiler

Compiled 36 to 28 computations (22.2% saved)

sample7.0s (46.1%)

Symmetry

(sort x y z t)

Results

2.7s	4564×	body	512	valid
2.2s	9880×	body	128	invalid
1.4s	1792×	body	1024	valid
413.0ms	1044×	body	256	valid
175.0ms	856×	body	128	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

798×	`rules-42_binary64`
798×	`rules-43_binary64`
492×	`rules-40_binary64`
492×	`rules-41_binary64`
284×	`rules-21_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	145	50
2	442	50
3	1954	50
4	4566	50
5	4855	50

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

5.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	5.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 136 to 100 computations (26.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	2.3b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	6.1b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series82.0ms (0.5%)

Counts

4 → 4

Calls

4 calls:

30.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
22.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
15.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
14.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite106.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

244×	`prod-diff_binary64`
236×	`egg-rr`
220×	`log1p-expm1-u_binary64`
220×	`expm1-log1p-u_binary64`
217×	`add-sqr-sqrt_binary64`

Counts

4 → 236

Calls

4 calls:

98.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
98.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
98.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
98.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	531	44
2	4835	44
3	5195	44
0	0	0
1	0	0

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

25×	`fma-neg_binary64`
21×	`rules-13_binary64`
18×	`rules-40_binary64`
18×	`rules-41_binary64`
18×	`rules-42_binary64`

Counts

240 → 237

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	4
1	8	4
2	16	4
3	22	4
4	35	4
5	58	4
6	76	4
7	88	4
8	97	4
9	101	4
10	114	4
11	5	4

prune565.0ms (3.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	224	13	237
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	225	13	238

Error

5.5b

Counts

238 → 13

Alt Table

Status	Error	Program
	5.9b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (+.f64 1 x)) 1 (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (.f64 x x)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 x))) (sqrt.f64 (cbrt.f64 (.f64 x x))) (.f64 (sqrt.f64 (cbrt.f64 x)) (sqrt.f64 (cbrt.f64 (*.f64 x x)))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	42.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) (fma.f64 (neg.f64 (pow.f64 z 1/4)) (pow.f64 z 1/4) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	16.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (.f64 y y)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 y))) (sqrt.f64 (cbrt.f64 (.f64 y y))) (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (*.f64 y y))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	39.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 1 x) (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 x))) (cbrt.f64 x) (.f64 (cbrt.f64 (sqrt.f64 x)) (cbrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	41.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (sqrt.f64 (+.f64 z 1))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (fma.f64 (neg.f64 (pow.f64 y 1/4)) (pow.f64 y 1/4) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	5.7b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	13.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (pow.f64 (+.f64 z 1) 3/2) (pow.f64 z 3/2)) (+.f64 (+.f64 z 1) (+.f64 z (sqrt.f64 (*.f64 (+.f64 z 1) z)))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 (+.f64 1 y) (+.f64 y (sqrt.f64 (*.f64 (+.f64 1 y) y)))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 12837 to 7768 computations (39.5% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	3.9b	(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x)))
	6.1b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
✓	60.7b	(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))

series21.0ms (0.1%)

Counts

2 → 2

Calls

2 calls:

13.0ms	(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x)))
8.0ms	(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))

rewrite138.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

342×	`fma-udef_binary64`
329×	`prod-diff_binary64`
223×	`expm1-udef_binary64`
223×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`

Counts

2 → 80

Calls

2 calls:

136.0ms	(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x)))
136.0ms	(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	344	28
2	3590	28
3	5000	28
4	4828	28
5	4817	28
0	0	0
1	0	0

simplify41.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

62×	`fma-neg_binary64`
49×	`rules-11_binary64`
44×	`rules-40_binary64`
44×	`rules-41_binary64`
44×	`rules-42_binary64`

Counts

82 → 83

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	6	12
1	33	12
2	64	12
3	121	12
4	151	12
5	172	12
6	202	10
7	202	10
8	202	10
9	210	10
10	7	10

prune903.0ms (6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	202	13	215

Error

5.5b

Counts

215 → 13

Alt Table

Status	Error	Program
▶	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))) 1)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	13.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (pow.f64 (+.f64 z 1) 3/2) (pow.f64 z 3/2)) (+.f64 (+.f64 z 1) (+.f64 z (sqrt.f64 (*.f64 (+.f64 z 1) z)))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	16.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (.f64 y y)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 y))) (sqrt.f64 (cbrt.f64 (.f64 y y))) (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (*.f64 y y))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	39.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 1 x) (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (fma.f64 (neg.f64 (pow.f64 y 1/4)) (pow.f64 y 1/4) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) 2) (+.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) 2)))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 (+.f64 1 y) (+.f64 y (sqrt.f64 (*.f64 (+.f64 1 y) y)))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (+.f64 1 (/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))) (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	42.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) (fma.f64 (neg.f64 (pow.f64 z 1/4)) (pow.f64 z 1/4) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	41.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (sqrt.f64 (+.f64 z 1))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 13838 to 8877 computations (35.9% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	3.9b	(fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x)))
	6.1b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
	60.7b	(fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x))

prune827.0ms (5.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	200	2	202
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	202	13	215

Error

5.5b

Counts

215 → 13

Alt Table

Status	Error	Program
✓	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2)) (sqrt.f64 (cbrt.f64 (+.f64 1 x))) (neg.f64 (sqrt.f64 x))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))) 1)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	13.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (pow.f64 (+.f64 z 1) 3/2) (pow.f64 z 3/2)) (+.f64 (+.f64 z 1) (+.f64 z (sqrt.f64 (*.f64 (+.f64 z 1) z)))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	16.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (.f64 y y)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 y))) (sqrt.f64 (cbrt.f64 (.f64 y y))) (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (*.f64 y y))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	39.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	5.8b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2)) (+.f64 (+.f64 1 x) (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (neg.f64 (sqrt.f64 x)) (+.f64 1 (/.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x))))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))) 1)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (fma.f64 (neg.f64 (pow.f64 y 1/4)) (pow.f64 y 1/4) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 (+.f64 1 y) (+.f64 y (sqrt.f64 (*.f64 (+.f64 1 y) y)))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	42.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) (fma.f64 (neg.f64 (pow.f64 z 1/4)) (pow.f64 z 1/4) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	41.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (sqrt.f64 (+.f64 z 1))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.9b	(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) 2) (+.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) 2)))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))) 1)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 14603 to 9655 computations (33.9% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))
	2.3b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.7b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
	6.1b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series9.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))

rewrite59.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

767×	`log1p-expm1-u_binary64`
767×	`expm1-log1p-u_binary64`
465×	`prod-diff_binary64`
85×	`egg-rr`
77×	`add-sqr-sqrt_binary64`

Counts

1 → 85

Calls

1 calls:

57.0ms

(-.f64 (pow.f64 (+.f64 1 x) 3/2) (pow.f64 x 3/2))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	193	13
2	2175	13
3	5727	13
0	0	0
1	0	0

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

990×	`rules-43_binary64`
571×	`fma-def_binary64`
453×	`rules-40_binary64`
453×	`rules-42_binary64`
451×	`rules-41_binary64`

Counts

97 → 107

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	62	402
1	419	394
2	1696	314
3	4913	274
4	4872	274

prune1.0s (6.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	283	2	285
Fresh	1	10	11
Picked	1	0	1
Done	1	0	1
Total	286	12	298

Error

2.4b

Counts

298 → 12

Alt Table

Status	Error	Program
	16.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (.f64 y y)))))) (fma.f64 (neg.f64 (sqrt.f64 (cbrt.f64 y))) (sqrt.f64 (cbrt.f64 (.f64 y y))) (.f64 (sqrt.f64 (cbrt.f64 y)) (sqrt.f64 (cbrt.f64 (*.f64 y y))))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	39.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 1) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 2) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) (fma.f64 (neg.f64 (pow.f64 y 1/4)) (pow.f64 y 1/4) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	13.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (pow.f64 (+.f64 z 1) 3/2) (pow.f64 z 3/2)) (+.f64 (+.f64 z 1) (+.f64 z (sqrt.f64 (*.f64 (+.f64 z 1) z)))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2)) (+.f64 (+.f64 1 y) (+.f64 y (sqrt.f64 (*.f64 (+.f64 1 y) y)))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	42.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) (fma.f64 (neg.f64 (pow.f64 z 1/4)) (pow.f64 z 1/4) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	56.8b	(+.f64 (+.f64 (+.f64 (/.f64 (fma.f64 3/2 (sqrt.f64 x) (.f64 3/8 (sqrt.f64 (/.f64 1 x)))) (+.f64 (+.f64 1 x) (+.f64 x (sqrt.f64 (.f64 (+.f64 1 x) x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	56.8b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (.f64 3/8 (sqrt.f64 (/.f64 1 x))) (.f64 3/2 (sqrt.f64 x))) (+.f64 (+.f64 1 x) (+.f64 x (sqrt.f64 (*.f64 (+.f64 1 x) x))))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	18.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (cbrt.f64 (+.f64 1 y)) (cbrt.f64 (sqrt.f64 (+.f64 1 y))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	41.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (fma.f64 (cbrt.f64 (+.f64 z 1)) (cbrt.f64 (sqrt.f64 (+.f64 z 1))) (neg.f64 (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.9b	(+.f64 (+.f64 (+.f64 (+.f64 (*.f64 (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) 2) (+.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) (/.f64 (sqrt.f64 (+.f64 x 1)) (pow.f64 (cbrt.f64 (neg.f64 (sqrt.f64 x))) 2)))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 (neg.f64 (pow.f64 x 1/4)) (pow.f64 x 1/4) (sqrt.f64 x)))) 1)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 18437 to 12237 computations (33.6% saved)

regimes1.7s (11.1%)

Accuracy

Total 0.2b remaining (8.7%)

Threshold costs 0.2b (8.7%)

Counts

106 → 2

Compiler

Compiled 57243 to 42721 computations (25.4% saved)

bsearch6.0ms (0%)

Compiler: Compiled 19 to 15 computations (21.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	162
1	54	162
2	53	162

end2.0s (13.5%)

Compiler: Compiled 1007 to 732 computations (27.3% saved)

Iter	Nodes	Cost
0	6	12
1	33	12
2	64	12
3	121	12
4	151	12
5	172	12
6	202	10
7	202	10
8	202	10
9	210	10
10	7	10

Iter	Nodes	Cost
0	6	12
1	33	12
2	64	12
3	121	12
4	151	12
5	172	12
6	202	10
7	202	10
8	202	10
9	210	10
10	7	10

Details

analyze392.0ms (2.6%)

sample7.0s (46.1%)

simplify60.0ms (0.4%)

prune3.0ms (0%)

localize19.0ms (0.1%)

series82.0ms (0.5%)

rewrite106.0ms (0.7%)

simplify18.0ms (0.1%)

prune565.0ms (3.7%)

localize33.0ms (0.2%)

series21.0ms (0.1%)

rewrite138.0ms (0.9%)

simplify41.0ms (0.3%)

prune903.0ms (6%)

localize39.0ms (0.3%)

prune827.0ms (5.5%)

localize33.0ms (0.2%)

series9.0ms (0.1%)

rewrite59.0ms (0.4%)

simplify65.0ms (0.4%)

prune1.0s (6.6%)

regimes1.7s (11.1%)

bsearch6.0ms (0%)

simplify3.0ms (0%)

end2.0s (13.5%)

Profiling

Iter	Nodes	Cost
0	6	12
1	33	12
2	64	12
3	121	12
4	151	12
5	172	12
6	202	10
7	202	10
8	202	10
9	210	10
10	7	10