Details

analyze620.0ms (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
4.6%	9.4%	86%	7
5.6%	8.4%	86%	8
6.6%	7.4%	86%	9
9.3%	4.7%	86%	10
10.1%	4%	86%	11
10.8%	3.3%	86%	12
11.6%	2.5%	86%	13
12%	2.1%	86%	14

Compiler

Compiled 67 to 35 computations (47.8% saved)

sample1.5s (7.3%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 134 to 70 computations (47.8% saved)

preprocess28.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

915×	`distribute-rgt-in_binary64`
897×	`distribute-lft-in_binary64`
304×	`fma-def_binary64`
241×	`times-frac_binary64`
202×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	300
1	246	268
2	1026	268
0	3	3
1	3	3

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort alpha beta)

Compiler

Compiled 56 to 27 computations (51.8% saved)

simplify19.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

684×	`associate-+l+_binary64`
483×	`associate-l_binary64`
418×	`associate-r_binary64`
369×	`times-frac_binary64`
337×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	75
1	67	67
2	332	67
3	2169	67

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

47.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	53.1b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))
▶	48.1b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))

Status

Error

Program

53.1b

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

▶

48.1b

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

Compiler

Compiled 315 to 155 computations (50.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta)))
✓	0.1b	(*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))
✓	5.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
✓	46.0b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))

series1.6s (7.6%)

Counts

4 → 144

Calls

36 calls:

351.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))	beta
344.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))	alpha
290.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))	i
133.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))	alpha
129.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))	beta

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

211×	`add-sqr-sqrt_binary64`
200×	`add-cbrt-cube_binary64`
200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
195×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	161
1	411	146

Stop Event

1×	node limit

Counts

4 → 107

simplify390.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
511×	`times-frac_binary64`
68×	`sub-neg_binary64`
56×	`sqr-pow_binary64`
12×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2952	51722

Stop Event

1×	node limit

Counts

251 → 283

prune2.0s (9.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	276	7	283
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	278	7	285

Error

12.3b

Counts

285 → 7

Alt Table

Status	Error	Program
	48.1b	(/.f64 (.f64 i (+.f64 (+.f64 i alpha) beta)) (.f64 (/.f64 (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i 2 beta))))
	56.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
	48.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))) 2) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
	41.0b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))))) 2)
▶	18.5b	1/16
	40.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	57.4b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))

Compiler

Compiled 76086 to 46681 computations (38.6% saved)

localize0.0ms (0%)

prune9.0ms (0%)

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

12.3b

Counts

7 → 7

Alt Table

Status	Error	Program
	48.1b	(/.f64 (.f64 i (+.f64 (+.f64 i alpha) beta)) (.f64 (/.f64 (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i 2 beta))))
	56.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
	48.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))) 2) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
	41.0b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))))) 2)
✓	18.5b	1/16
▶	40.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	57.4b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))

Compiler

Compiled 470 to 276 computations (41.3% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta)))
✓	5.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓	31.0b	(/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))
✓	35.8b	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta)))

series1.6s (8%)

Counts

3 → 108

Calls

27 calls:

354.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))	alpha
343.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))	beta
321.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))	i
174.0ms	(/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))	alpha
137.0ms	(/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))	beta

rewrite39.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

253×	`add-sqr-sqrt_binary64`
244×	`log1p-expm1-u_binary64`
244×	`expm1-log1p-u_binary64`
243×	`add-cbrt-cube_binary64`
235×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	126
1	541	126

Stop Event

1×	node limit

Counts

3 → 51

simplify337.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
608×	`associate-/l*_binary64`
511×	`times-frac_binary64`
56×	`sqr-pow_binary64`
56×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2937	50670

Stop Event

1×	node limit

Counts

159 → 192

prune1.2s (6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	267	1	268
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	267	8	275

Error

12.3b

Counts

275 → 8

Alt Table

Status	Error	Program
	48.1b	(/.f64 (.f64 i (+.f64 (+.f64 i alpha) beta)) (.f64 (/.f64 (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i 2 beta))))
	56.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
	48.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))) 2) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
	56.8b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
▶	41.0b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))))) 2)
✓	18.5b	1/16
✓	40.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	57.4b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))

Compiler

Compiled 76423 to 47579 computations (37.7% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.5b	(sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))))
✓	5.8b	(.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))))
	31.0b	(/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))
	35.8b	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta)))

series6.4s (31%)

Counts

2 → 68

Calls

18 calls:

2.4s	(sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))))	alpha
2.1s	(sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))))	beta
559.0ms	(sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))))	i
359.0ms	(.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))))	alpha
338.0ms	(.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))))	beta

rewrite39.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

233×	`add-sqr-sqrt_binary64`
224×	`log1p-expm1-u_binary64`
224×	`expm1-log1p-u_binary64`
223×	`add-cbrt-cube_binary64`
217×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	126
1	464	126

Stop Event

1×	node limit

Counts

2 → 45

simplify576.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

333×	`times-frac_binary64`
12×	`cube-mult_binary64`
12×	`unpow3_binary64`
9×	`unpow2_binary64`
3×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4716	90074

Stop Event

1×	node limit

Counts

113 → 140

prune3.0s (14.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	268	1	269
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	268	9	277

Error

8.0b

Counts

277 → 9

Alt Table

Status	Error	Program
	48.1b	(/.f64 (.f64 i (+.f64 (+.f64 i alpha) beta)) (.f64 (/.f64 (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i 2 beta))))
	56.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
	57.4b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	53.2b	(pow.f64 (.f64 (/.f64 1 beta) (sqrt.f64 (.f64 (+.f64 i alpha) i))) 2)
	48.2b	(.f64 (pow.f64 (sqrt.f64 (.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))) 2) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
	56.8b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
✓	41.0b	(pow.f64 (sqrt.f64 (.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (*.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))))) 2)
✓	18.5b	1/16
✓	40.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))

Compiler

Compiled 146843 to 91895 computations (37.4% saved)

regimes831.0ms (4%)

Accuracy

Total 9.1b remaining (63.4%)

Threshold costs 0b (0%)

Counts

103 → 4

Compiler

Compiled 18432 to 11445 computations (37.9% saved)

bsearch78.0ms (0.4%)

Algorithm

3×	binary-search

Calls

3 calls:

29.0ms	beta
23.0ms	beta
19.0ms	beta

Steps

Iters

Point

Range

4.095819014891881e+181

∈ [

4.0308338655912195e+181

1.3020703395317232e+183

]

1.4424082428851503e+139

∈ [

1.8218278862426e+138

1.4704200825036452e+139

]

3.9444340291518456e+118

∈ [

3.911858189100447e+118

1.246332846140392e+121

]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	145
1	77	145
2	84	145
3	104	145
4	117	145
5	133	145
6	143	145
7	149	145
8	151	145

Stop Event

1×

saturated

end192.0ms (0.9%)

Stop Event

1×

fuel

Compiler

Compiled 668 to 422 computations (36.8% saved)

Iter	Nodes	Cost
0	56	145
1	77	145
2	84	145
3	104	145
4	117	145
5	133	145
6	143	145
7	149	145
8	151	145

Iter	Nodes	Cost
0	56	145
1	77	145
2	84	145
3	104	145
4	117	145
5	133	145
6	143	145
7	149	145
8	151	145

Details

analyze620.0ms (3%)

sample1.5s (7.3%)

preprocess28.0ms (0.1%)

simplify19.0ms (0.1%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series1.6s (7.6%)

rewrite56.0ms (0.3%)

simplify390.0ms (1.9%)

prune2.0s (9.6%)

localize0.0ms (0%)

prune9.0ms (0%)

localize21.0ms (0.1%)

series1.6s (8%)

rewrite39.0ms (0.2%)

simplify337.0ms (1.6%)

prune1.2s (6%)

localize18.0ms (0.1%)

series6.4s (31%)

rewrite39.0ms (0.2%)

simplify576.0ms (2.8%)

prune3.0s (14.7%)

regimes831.0ms (4%)

bsearch78.0ms (0.4%)

simplify9.0ms (0%)

end192.0ms (0.9%)

Profiling

Iter	Nodes	Cost
0	56	145
1	77	145
2	84	145
3	104	145
4	117	145
5	133	145
6	143	145
7	149	145
8	151	145