Details

analyze52.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 67 to 35 computations (47.8% saved)

sample1.9s (11.7%)

Symmetry

(sort alpha beta)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-+l+_binary64`
492×	`associate-l_binary64`
422×	`associate-r_binary64`
369×	`times-frac_binary64`
336×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	75
1	67	67
2	293	67
3	1612	67
4	4979	67
5	5035	67

prune4.0ms (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

53.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	53.3b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Status

Error

Program

▶

53.3b

(/.f64 (/.f64 (*.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 203 to 89 computations (56.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	0.1b	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	32.7b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	45.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))

series1.3s (7.9%)

Counts

4 → 144

Calls

4 calls:

1.1s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
150.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
38.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
13.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite101.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

582×	`prod-diff_binary64`
192×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`

Counts

4 → 116

Calls

4 calls:

96.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
96.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
96.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
96.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	131
1	381	131
2	4911	131
3	6081	131

simplify363.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
489×	`associate-/l*_binary64`
336×	`associate-/r*_binary64`
333×	`times-frac_binary64`
53×	`sqr-pow_binary64`

Counts

260 → 271

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2376	40163
1	5421	40163

prune1.2s (7.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	264	7	271
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	7	272

Error

7.1b

Counts

272 → 7

Alt Table

Status	Error	Program
	36.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))
	53.5b	(exp.f64 (log.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))
▶	15.8b	1/16
	35.7b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	35.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	52.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	35.7b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 59302 to 35615 computations (39.9% saved)

localize0.0ms (0%)

prune10.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

7.1b

Counts

7 → 7

Alt Table

Status	Error	Program
	36.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))
	53.5b	(exp.f64 (log.f64 (/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))
✓	15.8b	1/16
	35.7b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	35.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	52.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	35.7b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 570 to 294 computations (48.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
✓	2.4b	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))
✓	32.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	36.5b	(/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

series1.5s (9.3%)

Counts

4 → 144

Calls

4 calls:

1.1s	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
160.0ms	(/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
148.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))
102.0ms	(/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))

rewrite94.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

255×	`prod-diff_binary64`
205×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
190×	`add-cbrt-cube_binary64`

Counts

4 → 125

Calls

4 calls:

87.0ms	(/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
87.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))))
87.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
87.0ms	(/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	151
1	420	148
2	4761	148
3	5211	148

simplify911.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

954×	`fma-def_binary64`
361×	`times-frac_binary64`
76×	`sub-neg_binary64`
67×	`sqr-pow_binary64`
13×	`unpow2_binary64`

Counts

269 → 313

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3163	49600
1	5099	49600

prune1.6s (9.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	310	3	313
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	313	7	320

Error

7.1b

Counts

320 → 7

Alt Table

Status	Error	Program
▶	35.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	15.8b	1/16
	35.7b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))))) 2) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	35.9b	(exp.f64 (log.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))
✓	35.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	52.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	35.7b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 72189 to 43081 computations (40.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)
✓	2.4b	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2))
✓	31.5b	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	32.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

series2.0s (12.5%)

Counts

4 → 112

Calls

4 calls:

1.1s	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
651.0ms	(pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)
143.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2))
111.0ms	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

rewrite85.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`prod-diff_binary64`
212×	`add-sqr-sqrt_binary64`
202×	`log1p-expm1-u_binary64`
202×	`expm1-log1p-u_binary64`
197×	`add-cbrt-cube_binary64`

Counts

4 → 99

Calls

4 calls:

81.0ms	(pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)
81.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2))
81.0ms	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
81.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	157
1	436	143
2	4815	143
3	5199	143

simplify362.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
529×	`associate-/l*_binary64`
339×	`times-frac_binary64`
63×	`sqr-pow_binary64`
60×	`sub-neg_binary64`

Counts

211 → 262

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2706	41380
1	5385	41380

prune1.1s (6.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	262	7	269

Error

7.1b

Counts

269 → 7

Alt Table

Status	Error	Program
✓	35.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (pow.f64 (/.f64 1 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	15.8b	1/16
	35.7b	(/.f64 (pow.f64 (/.f64 (sqrt.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))))) 2) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	35.9b	(exp.f64 (log.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))
	35.7b	(.f64 (/.f64 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) -2) 1) (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
✓	35.7b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	52.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 62216 to 37820 computations (39.2% saved)

regimes3.3s (20.1%)

Accuracy

Total 1.4b remaining (11.4%)

Threshold costs 0b (0%)

Counts

171 → 4

Compiler

Compiled 66036 to 38961 computations (41% saved)

bsearch80.0ms (0.5%)

Steps

Iters	Range		Point
5	1.9926835810438144e+146	4.495612386708377e+146	2.587302964673011e+146
5	1.6326922672736569e+100	6.374934685865714e+100	3.1729621267394858e+100
5	2.643871909577531e+69	6.514962625407384e+69	3.1189906262604905e+69

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	186
1	50	186
2	50	186

end173.0ms (1.1%)

Remove: (sort alpha beta)
Compiler: Compiled 780 to 398 computations (49% saved)

Details

analyze52.0ms (0.3%)

sample1.9s (11.7%)

simplify43.0ms (0.3%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series1.3s (7.9%)

rewrite101.0ms (0.6%)

simplify363.0ms (2.2%)

prune1.2s (7.5%)

localize0.0ms (0%)

prune10.0ms (0.1%)

localize17.0ms (0.1%)

series1.5s (9.3%)

rewrite94.0ms (0.6%)

simplify911.0ms (5.6%)

prune1.6s (9.7%)

localize18.0ms (0.1%)

series2.0s (12.5%)

rewrite85.0ms (0.5%)

simplify362.0ms (2.2%)

prune1.1s (6.8%)

regimes3.3s (20.1%)

bsearch80.0ms (0.5%)

simplify4.0ms (0%)

end173.0ms (1.1%)

Profiling