Details

analyze768.0ms (4.8%)

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)

sample10.9s (68.8%)

Symmetry

(sort x y z t)

Results

4.5s	4624×	body	512	valid
3.3s	9904×	body	128	invalid
2.1s	1765×	body	1024	valid
647.0ms	1025×	body	256	valid
270.0ms	842×	body	128	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify56.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

699×	`fma-def_binary64`
529×	`associate-+r-_binary64`
510×	`associate-+l-_binary64`
481×	`associate--r+_binary64`
355×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	54	50
2	166	50
3	893	50
4	4070	50
5	4939	50
6	5040	50

prune4.0ms (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

6.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.1b	(+.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)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	4.7b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
✓	6.9b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series106.0ms (0.7%)

Counts

4 → 4

Calls

4 calls:

57.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
17.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
17.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
15.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite114.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

243×	`log1p-expm1-u_binary64`
243×	`expm1-log1p-u_binary64`
240×	`add-sqr-sqrt_binary64`
236×	`prod-diff_binary64`
227×	`add-cbrt-cube_binary64`

Counts

4 → 172

Calls

4 calls:

110.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
110.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
110.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
110.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	496	44
2	4958	44
3	5228	44
0	0	0
1	0	0

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

176 → 173

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	4
1	4	4
2	3	4

prune440.0ms (2.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	159	14	173
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	14	174

Error

4.4b

Counts

174 → 14

Alt Table

Status	Error	Program
	23.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 1/2) (neg.f64 (.f64 (sqrt.f64 x) 1))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (.f64 (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)))
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 1 (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)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 3))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	19.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 y))) (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) 2)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.5b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 y 1) y) (+.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)))
	6.1b	(+.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))) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) 2))
	6.0b	(+.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 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
▶	5.4b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	19.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.f64 (+.f64 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)) (-.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 (+.f64 1 x) x) (+.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)))

Compiler

Compiled 9189 to 5754 computations (37.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	3.1b	(-.f64 (+.f64 1 z) z)
	6.9b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))

series1.0ms (0%)

Counts

1 → 12

Calls

1 calls:

1.0ms

(-.f64 (+.f64 1 z) z)

rewrite92.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

677×	`prod-diff_binary64`
537×	`log1p-expm1-u_binary64`
537×	`expm1-log1p-u_binary64`
475×	`fma-udef_binary64`
259×	`fma-def_binary64`

Counts

1 → 1

Calls

1 calls:

92.0ms

(-.f64 (+.f64 1 z) z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	114	1
2	1281	1
3	4769	1
4	4702	1
5	4949	1
0	0	0
1	0	0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

13 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
1	4	12
2	3	12

prune436.0ms (2.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	127	4	131
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	132	13	145

Error

4.0b

Counts

145 → 13

Alt Table

Status	Error	Program
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 1 (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)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 3))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	19.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (+.f64 (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 y))) (sqrt.f64 (sqrt.f64 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 1/2) (neg.f64 (.f64 (sqrt.f64 x) 1))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (.f64 (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)))
	6.1b	(+.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))) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) 2))
	6.0b	(+.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 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	22.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	4.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	19.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (sqrt.f64 y)))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.f64 (+.f64 (+.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) 3)) (-.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 (+.f64 1 x) x) (+.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)))

Compiler

Compiled 7955 to 5042 computations (36.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.1b	(-.f64 (+.f64 1 z) z)
✓	5.4b	(-.f64 (+.f64 y 1) y)

series1.0ms (0%)

Counts

1 → 12

Calls

1 calls:

1.0ms

(-.f64 (+.f64 y 1) y)

rewrite46.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

628×	`log1p-expm1-u_binary64`
628×	`expm1-log1p-u_binary64`
549×	`prod-diff_binary64`
100×	`log1p-udef_binary64`
83×	`egg-rr`

Counts

1 → 83

Calls

1 calls:

44.0ms

(-.f64 (+.f64 y 1) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	7
2	1502	7
3	4971	7
0	0	0
1	0	0

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

95 → 84

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
1	4	12
2	3	12

prune541.0ms (3.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	172	12	184

Error

3.2b

Counts

184 → 12

Alt Table

Status	Error	Program
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 1 (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)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 3))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 y 1) y) (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.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))) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) 2))
▶	3.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.0b	(+.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 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 1/2) (neg.f64 (.f64 (sqrt.f64 x) 1))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (.f64 (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)))
	22.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	19.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (fma.f64 (cbrt.f64 (+.f64 y 1)) (cbrt.f64 (sqrt.f64 (+.f64 y 1))) (neg.f64 (sqrt.f64 y)))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.8b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.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)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 10784 to 6779 computations (37.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))
	1.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	1.7b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	3.1b	(-.f64 (+.f64 1 z) z)

series15.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

15.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))

rewrite49.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
84×	`add-sqr-sqrt_binary64`
79×	`add-cbrt-cube_binary64`
79×	`add-log-exp_binary64`

Counts

1 → 25

Calls

1 calls:

48.0ms

(/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	176	14
2	2142	14
3	5096	14
0	0	0
1	0	0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Counts

26 → 26

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1
2	3	1

prune382.0ms (2.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	111	14	125

Error

3.1b

Counts

125 → 14

Alt Table

Status	Error	Program
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 1 (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)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) 3))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	3.6b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 (/.f64 1 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (cbrt.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)) -2)))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.0b	(+.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 (-.f64 (+.f64 1 t) t) (+.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))
	3.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y)))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (exp.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) 1)) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	22.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) 1) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.0b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 x)) 2) 1/2) (pow.f64 (cbrt.f64 (+.f64 1 x)) 1/2) (neg.f64 (.f64 (sqrt.f64 x) 1))) (fma.f64 (neg.f64 (sqrt.f64 x)) 1 (.f64 (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)))
	4.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3) 1/3)) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.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))) (pow.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))) 2))
	3.9b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (exp.f64 (neg.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))) (/.f64 (-.f64 (+.f64 1 z) z) (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.1b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 6474 to 4195 computations (35.2% saved)

regimes1.4s (8.9%)

Accuracy

Total 0.6b remaining (20.7%)

Threshold costs 0.6b (20.7%)

Counts

92 → 1

Compiler

Compiled 53537 to 40216 computations (24.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	56
1	42	56
2	49	56
3	53	56
4	55	56
5	54	56

end370.0ms (2.3%)

Remove: (sort x y z t)
Compiler: Compiled 776 to 598 computations (22.9% saved)

Details

analyze768.0ms (4.8%)

sample10.9s (68.8%)

simplify56.0ms (0.4%)

prune4.0ms (0%)

localize20.0ms (0.1%)

series106.0ms (0.7%)

rewrite114.0ms (0.7%)

simplify10.0ms (0.1%)

prune440.0ms (2.8%)

localize24.0ms (0.2%)

series1.0ms (0%)

rewrite92.0ms (0.6%)

simplify8.0ms (0%)

prune436.0ms (2.7%)

localize24.0ms (0.2%)

series1.0ms (0%)

rewrite46.0ms (0.3%)

simplify8.0ms (0.1%)

prune541.0ms (3.4%)

localize22.0ms (0.1%)

series15.0ms (0.1%)

rewrite49.0ms (0.3%)

simplify7.0ms (0%)

prune382.0ms (2.4%)

regimes1.4s (8.9%)

simplify3.0ms (0%)

end370.0ms (2.3%)

Profiling