Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 44 to 29 computations (34.1% saved)

sample1.4s (16%)

Symmetry

(sort alpha beta)

Results

1.4s

8256×

body

128

valid

Compiler

Compiled 125 to 82 computations (34.4% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

689×	`distribute-rgt-in_binary64`
661×	`distribute-lft-in_binary64`
470×	`associate-l_binary64`
388×	`associate-+r+_binary64`
387×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	40
1	36	38
2	117	38
3	625	37
4	4291	37
5	4944	37

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (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

0.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	2.4b	(.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))

Status

Error

Program

▶

2.1b

(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

2.4b

(*.f64 (/.f64 (+.f64 alpha 1) (+.f64 beta (+.f64 alpha 3))) (/.f64 (+.f64 beta 1) (*.f64 (+.f64 alpha (+.f64 beta 2)) (+.f64 alpha (+.f64 beta 2)))))

Compiler

Compiled 190 to 127 computations (33.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)
✓	0.0b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
✓	0.1b	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
✓	1.9b	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

series141.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

73.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
41.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
20.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))
7.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)

rewrite45.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

174×	`add-sqr-sqrt_binary64`
171×	`log1p-expm1-u_binary64`
171×	`expm1-log1p-u_binary64`
168×	`add-cbrt-cube_binary64`
162×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	100
1	349	82

Stop Event

1×	node limit

Counts

4 → 140

Calls

4 calls:

42.0ms	(+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1)
42.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (*.f64 2 1)))
42.0ms	(/.f64 (/.f64 (/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
42.0ms	(/.f64 (+.f64 (+.f64 (+.f64 alpha beta) (.f64 beta alpha)) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1)))

simplify110.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

881×	`times-frac_binary64`
840×	`fma-def_binary64`
344×	`+-commutative_binary64`
282×	`associate-+r+_binary64`
189×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	851	9100
1	3049	9060

Stop Event

1×	node limit

Counts

236 → 234

prune505.0ms (5.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	227	7	234
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	229	7	236

Error

0.0b

Counts

236 → 7

Alt Table

Status	Error	Program
	2.2b	(/.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
▶	2.2b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
	2.9b	(*.f64 (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))) (/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	4.3b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (+.f64 alpha beta) 3) 2))) (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	29.8b	(/.f64 (-.f64 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) (fma.f64 2 (.f64 (/.f64 alpha beta) (/.f64 alpha beta)) (fma.f64 5 (/.f64 alpha (.f64 beta beta)) (/.f64 3 (.f64 beta beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	3.7b	(pow.f64 (*.f64 (/.f64 (+.f64 (+.f64 alpha beta) 3) (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) -1)
	3.7b	(/.f64 (/.f64 (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 (pow.f64 (+.f64 alpha beta) 2) -4)) (+.f64 (+.f64 alpha beta) -2)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

Compiler

Compiled 16759 to 11462 computations (31.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
✓	0.1b	(/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2)))
✓	0.3b	(pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2)
✓	1.9b	(sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)))

series508.0ms (5.7%)

Counts

4 → 48

Calls

4 calls:

260.0ms	(pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2)
125.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2)))
70.0ms	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
53.0ms	(sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)))

rewrite45.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

184×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`
173×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	94
1	394	90

Stop Event

1×	node limit

Counts

4 → 108

Calls

4 calls:

42.0ms	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
42.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2)))
42.0ms	(pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2)
42.0ms	(sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)))

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

819×	`times-frac_binary64`
748×	`fma-def_binary64`
228×	`+-commutative_binary64`
187×	`*-commutative_binary64`
179×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	677	6543
1	2456	6448

Stop Event

1×	node limit

Counts

156 → 185

prune376.0ms (4.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	185	7	192

Error

0.0b

Counts

192 → 7

Alt Table

Status	Error	Program
▶	2.2b	(/.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
✓	2.2b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
	2.9b	(*.f64 (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))) (/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	4.3b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (+.f64 alpha beta) 3) 2))) (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	29.8b	(/.f64 (-.f64 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) (fma.f64 2 (.f64 (/.f64 alpha beta) (/.f64 alpha beta)) (fma.f64 5 (/.f64 alpha (.f64 beta beta)) (/.f64 3 (.f64 beta beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	3.7b	(pow.f64 (*.f64 (/.f64 (+.f64 (+.f64 alpha beta) 3) (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) -1)
	3.7b	(/.f64 (/.f64 (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 (pow.f64 (+.f64 alpha beta) 2) -4)) (+.f64 (+.f64 alpha beta) -2)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

Compiler

Compiled 12805 to 9329 computations (27.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1)
✓	0.1b	(/.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
✓	0.3b	(exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2)))))
✓	1.9b	(/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2)))

series782.0ms (8.7%)

Counts

4 → 96

Calls

4 calls:

456.0ms	(/.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
169.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1)
134.0ms	(exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2)))))
21.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2)))

rewrite46.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

205×	`add-sqr-sqrt_binary64`
203×	`expm1-log1p-u_binary64`
202×	`log1p-expm1-u_binary64`
197×	`add-cbrt-cube_binary64`
192×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	102
1	434	98

Stop Event

1×	node limit

Counts

4 → 125

Calls

4 calls:

42.0ms	(-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1)
42.0ms	(/.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
42.0ms	(exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2)))))
42.0ms	(/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2)))

simplify194.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-+r+_binary64`
388×	`fma-def_binary64`
353×	`associate-/r*_binary64`
262×	`associate-*r/_binary64`
214×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1690	30055

Stop Event

1×	node limit

Counts

221 → 210

prune1.0s (11.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	210	0	210
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	210	7	217

Error

0.0b

Counts

217 → 7

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
✓	2.2b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
▶	2.9b	(*.f64 (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))) (/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	4.3b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (+.f64 alpha beta) 3) 2))) (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	29.8b	(/.f64 (-.f64 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) (fma.f64 2 (.f64 (/.f64 alpha beta) (/.f64 alpha beta)) (fma.f64 5 (/.f64 alpha (.f64 beta beta)) (/.f64 3 (.f64 beta beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	3.7b	(pow.f64 (*.f64 (/.f64 (+.f64 (+.f64 alpha beta) 3) (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) -1)
	3.7b	(/.f64 (/.f64 (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 (pow.f64 (+.f64 alpha beta) 2) -4)) (+.f64 (+.f64 alpha beta) -2)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

Compiler

Compiled 42030 to 30976 computations (26.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3)))
✓	0.6b	(*.f64 (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))) (/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))))
✓	0.6b	(/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3)))
	1.9b	(/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2)))

series253.0ms (2.8%)

Counts

3 → 40

Calls

3 calls:

120.0ms

(/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3)))

80.0ms

(*.f64 (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))) (/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))))

53.0ms

(/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3)))

rewrite45.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

215×	`add-sqr-sqrt_binary64`
208×	`log1p-expm1-u_binary64`
208×	`expm1-log1p-u_binary64`
206×	`add-cbrt-cube_binary64`
201×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	93
1	434	87

Stop Event

1×	node limit

Counts

3 → 110

Calls

3 calls:

42.0ms

(/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3)))

42.0ms

(*.f64 (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))) (/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))))

41.0ms

(/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3)))

simplify103.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
672×	`associate-/l*_binary64`
270×	`+-commutative_binary64`
237×	`fma-def_binary64`
229×	`associate-+r+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	753	8391
1	2836	8156

Stop Event

1×	node limit

Counts

150 → 172

prune571.0ms (6.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	232	7	239

Error

0.0b

Counts

239 → 7

Alt Table

Status	Error	Program
✓	2.2b	(/.f64 (/.f64 (-.f64 (exp.f64 (log1p.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))))) 1) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
✓	2.2b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (+.f64 alpha (+.f64 beta 2))) 2) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))
✓	2.9b	(*.f64 (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))) (/.f64 (/.f64 1 (+.f64 alpha (+.f64 beta 2))) (sqrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	4.3b	(*.f64 (/.f64 1 (cbrt.f64 (pow.f64 (+.f64 (+.f64 alpha beta) 3) 2))) (/.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) (cbrt.f64 (+.f64 (+.f64 alpha beta) 3))))
	29.8b	(/.f64 (-.f64 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) (fma.f64 2 (.f64 (/.f64 alpha beta) (/.f64 alpha beta)) (fma.f64 5 (/.f64 alpha (.f64 beta beta)) (/.f64 3 (.f64 beta beta))))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 1)) 1))
	3.7b	(pow.f64 (*.f64 (/.f64 (+.f64 (+.f64 alpha beta) 3) (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1))) (pow.f64 (+.f64 alpha (+.f64 beta 2)) 2)) -1)
	3.7b	(/.f64 (/.f64 (.f64 (/.f64 (+.f64 (+.f64 alpha beta) (fma.f64 alpha beta 1)) (+.f64 (pow.f64 (+.f64 alpha beta) 2) -4)) (+.f64 (+.f64 alpha beta) -2)) (+.f64 (+.f64 alpha beta) (.f64 2 1))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 1)) 1))

Compiler

Compiled 19595 to 14113 computations (28% saved)

regimes2.1s (24%)

Accuracy

Total 0.1b remaining (45.4%)

Threshold costs 0.1b (45.4%)

Counts

244 → 2

Compiler

Compiled 24533 to 17039 computations (30.5% saved)

bsearch27.0ms (0.3%)

Steps

Iters	Range		Point
4	1.5926801512152694e+128	4.455145655409914e+129	4.603857948514167e+128

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	95
1	49	95
2	52	95
3	54	95
4	55	95

Stop Event

1×

saturated

end407.0ms (4.6%)

Compiler: Compiled 518 to 317 computations (38.8% saved)

Details

analyze6.0ms (0.1%)

sample1.4s (16%)

simplify26.0ms (0.3%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series141.0ms (1.6%)

rewrite45.0ms (0.5%)

simplify110.0ms (1.2%)

prune505.0ms (5.6%)

localize15.0ms (0.2%)

series508.0ms (5.7%)

rewrite45.0ms (0.5%)

simplify90.0ms (1%)

prune376.0ms (4.2%)

localize18.0ms (0.2%)

series782.0ms (8.7%)

rewrite46.0ms (0.5%)

simplify194.0ms (2.2%)

prune1.0s (11.4%)

localize16.0ms (0.2%)

series253.0ms (2.8%)

rewrite45.0ms (0.5%)

simplify103.0ms (1.1%)

prune571.0ms (6.4%)

regimes2.1s (24%)

bsearch27.0ms (0.3%)

simplify4.0ms (0%)

end407.0ms (4.6%)

Profiling