Details

analyze359.0ms (3.3%)

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)

sample6.3s (59.3%)

Symmetry

(sort x y z t)

Results

2.4s	4529×	body	512	valid
2.0s	9929×	body	128	invalid
1.3s	1794×	body	1024	valid
386.0ms	1042×	body	256	valid
174.0ms	891×	body	128	valid

Compiler

Compiled 107 to 83 computations (22.4% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

531×	`associate-+r-_binary64`
502×	`associate-+l-_binary64`
451×	`associate--r+_binary64`
355×	`associate--r-_binary64`
345×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	50
1	54	50
2	168	50
3	975	50
4	4902	50

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

5.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	5.6b	(+.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)))
	6.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (-.f64 (-.f64 (sqrt.f64 (+.f64 1 z)) (sqrt.f64 z)) (+.f64 (sqrt.f64 y) (-.f64 (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 y))) (-.f64 (sqrt.f64 (+.f64 1 t)) (sqrt.f64 t))))))

Status

Error

Program

▶

5.6b

(+.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)))

6.0b

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

Compiler

Compiled 206 to 154 computations (25.2% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
✓	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	4.3b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
✓	5.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series44.0ms (0.4%)

Counts

4 → 4

Calls

4 calls:

12.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
12.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
10.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
10.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`log1p-expm1-u_binary64`
243×	`expm1-log1p-u_binary64`
240×	`add-sqr-sqrt_binary64`
239×	`add-cbrt-cube_binary64`
227×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	44
1	504	44

Stop Event

1×	node limit

Counts

4 → 108

Calls

4 calls:

37.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
37.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
37.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
36.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	4
1	4	4

Stop Event

1×

saturated

Counts

112 → 109

prune245.0ms (2.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	93	16	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	16	111

Error

4.4b

Counts

111 → 16

Alt Table

Status	Error	Program
	16.5b	(+.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 (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)))
	5.5b	(+.f64 (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 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 (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 (pow.f64 (*.f64 (+.f64 1 y) y) 1/2))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.f64 (+.f64 (+.f64 (pow.f64 (cbrt.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)))
	5.6b	(+.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))))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) 3)) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.4b	(+.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)))
	5.6b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.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)))
	5.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) 2)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	38.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 1 (sqrt.f64 (+.f64 z 1)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (cbrt.f64 z) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	37.3b	(+.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)))
▶	5.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 1 y) y) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.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 (fma.f64 (cbrt.f64 (+.f64 1 t)) (cbrt.f64 (sqrt.f64 (+.f64 1 t))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 t))) (cbrt.f64 t) (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))))
	5.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 z 1) z) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 5689 to 3642 computations (36% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
✓	2.9b	(-.f64 (+.f64 1 y) y)
	5.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series1.0ms (0%)

Counts

1 → 12

Calls

1 calls:

1.0ms

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

rewrite35.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

677×	`prod-diff_binary64`
537×	`log1p-expm1-u_binary64`
537×	`expm1-log1p-u_binary64`
84×	`log1p-udef_binary64`
57×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	1
2	1687	1

Stop Event

1×	node limit

Counts

1 → 1

Calls

1 calls:

34.0ms

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

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
1	4	12

Stop Event

1×

saturated

Counts

13 → 1

prune339.0ms (3.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	83	16	99

Error

4.1b

Counts

99 → 16

Alt Table

Status	Error	Program
	16.5b	(+.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 (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)))
	5.5b	(+.f64 (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 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 (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 (pow.f64 (*.f64 (+.f64 1 y) y) 1/2))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.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))))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) 3)) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.4b	(+.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)))
	5.6b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.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)))
	5.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (expm1.f64 (log1p.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) 2)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	38.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 1 (sqrt.f64 (+.f64 z 1)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (cbrt.f64 z) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	4.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (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 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	37.3b	(+.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)))
✓	5.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (/.f64 (-.f64 (+.f64 1 y) y) (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.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 (fma.f64 (cbrt.f64 (+.f64 1 t)) (cbrt.f64 (sqrt.f64 (+.f64 1 t))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 t))) (cbrt.f64 t) (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))))
	5.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 z 1) z) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 5110 to 3311 computations (35.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
	1.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	5.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series9.0ms (0.1%)

Counts

1 → 1

Calls

1 calls:

9.0ms

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

rewrite40.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

845×	`log1p-expm1-u_binary64`
845×	`expm1-log1p-u_binary64`
83×	`add-sqr-sqrt_binary64`
81×	`add-cbrt-cube_binary64`
78×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	178	14
2	2372	14

Stop Event

1×	node limit

Counts

1 → 25

Calls

1 calls:

39.0ms

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

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	1
1	4	1

Stop Event

1×

saturated

Counts

26 → 26

prune430.0ms (4%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	4	10	14
Picked	1	0	1
Done	1	0	1
Total	107	17	124

Error

4.1b

Counts

124 → 17

Alt Table

Status	Error	Program
	16.5b	(+.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 (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)))
	5.5b	(+.f64 (+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (fma.f64 (neg.f64 (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 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)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.8b	(+.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 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 y 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 y 1/4)) -1))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.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))))
	4.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	19.8b	(+.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)))
	5.6b	(+.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 (fma.f64 (cbrt.f64 (+.f64 1 t)) (cbrt.f64 (sqrt.f64 (+.f64 1 t))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 t))) (cbrt.f64 t) (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))))
	5.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 z 1) z) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	4.8b	(+.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 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) 2)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	38.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 1 (sqrt.f64 (+.f64 z 1)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (cbrt.f64 z) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
▶	4.5b	(+.f64 (+.f64 (+.f64 (/.f64 (-.f64 (+.f64 1 x) x) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2))) (-.f64 (+.f64 (+.f64 1 y) 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)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) 3)) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.f64 (+.f64 (+.f64 (+.f64 (fma.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.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)))

Compiler

Compiled 5879 to 3903 computations (33.6% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
✓	0.7b	(-.f64 (+.f64 1 x) x)
	1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
	5.2b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

series1.0ms (0%)

Counts

1 → 12

Calls

1 calls:

1.0ms

(-.f64 (+.f64 1 x) x)

rewrite28.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

677×	`prod-diff_binary64`
537×	`log1p-expm1-u_binary64`
537×	`expm1-log1p-u_binary64`
84×	`log1p-udef_binary64`
57×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	5	7
1	115	1
2	1687	1

Stop Event

1×	node limit

Counts

1 → 1

Calls

1 calls:

28.0ms

(-.f64 (+.f64 1 x) x)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1	12
1	4	12

Stop Event

1×

saturated

Counts

13 → 1

prune270.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	4	12	16
Picked	1	0	1
Done	0	0	0
Total	86	13	99

Error

1.0b

Counts

99 → 13

Alt Table

Status	Error	Program
	4.8b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (*.f64 (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 y 1/4)) -1) (pow.f64 (hypot.f64 (pow.f64 (+.f64 1 y) 1/4) (pow.f64 y 1/4)) -1))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.6b	(+.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))))
	4.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (expm1.f64 (log1p.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	19.8b	(+.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)))
	5.6b	(+.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 (fma.f64 (cbrt.f64 (+.f64 1 t)) (cbrt.f64 (sqrt.f64 (+.f64 1 t))) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 t))) (cbrt.f64 t) (.f64 (cbrt.f64 (sqrt.f64 t)) (cbrt.f64 t)))))
	5.3b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (/.f64 (-.f64 (+.f64 z 1) z) (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	1.5b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	16.5b	(+.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 (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)))
	5.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (*.f64 (cbrt.f64 (pow.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)) 2)) (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	38.2b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (+.f64 (fma.f64 1 (sqrt.f64 (+.f64 z 1)) (neg.f64 (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z)))) (fma.f64 (neg.f64 (cbrt.f64 (sqrt.f64 z))) (cbrt.f64 z) (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 z))))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y))) 3)) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
	6.6b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 1 y) 3/2) (pow.f64 y 3/2))) (-.f64 (+.f64 (+.f64 1 y) 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)))
	5.7b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (pow.f64 (cbrt.f64 (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) 3)) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))

Compiler

Compiled 4332 to 2851 computations (34.2% saved)

regimes1.3s (12.4%)

Accuracy

Total 0.5b remaining (41.5%)

Threshold costs 0.5b (41.5%)

Counts

97 → 1

Compiler

Compiled 52557 to 40267 computations (23.4% 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

Stop Event

1×

saturated

end1.0s (9.6%)

Compiler: Compiled 731 to 552 computations (24.5% saved)

Details

analyze359.0ms (3.3%)

sample6.3s (59.3%)

simplify24.0ms (0.2%)

prune5.0ms (0%)

localize29.0ms (0.3%)

series44.0ms (0.4%)

rewrite42.0ms (0.4%)

simplify7.0ms (0.1%)

prune245.0ms (2.3%)

localize23.0ms (0.2%)

series1.0ms (0%)

rewrite35.0ms (0.3%)

simplify7.0ms (0.1%)

prune339.0ms (3.2%)

localize21.0ms (0.2%)

series9.0ms (0.1%)

rewrite40.0ms (0.4%)

simplify6.0ms (0.1%)

prune430.0ms (4%)

localize24.0ms (0.2%)

series1.0ms (0%)

rewrite28.0ms (0.3%)

simplify7.0ms (0.1%)

prune270.0ms (2.5%)

regimes1.3s (12.4%)

simplify3.0ms (0%)

end1.0s (9.6%)

Profiling