Details

analyze110.0ms (0.5%)

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)

sample3.0s (13.1%)

Symmetry

(sort alpha beta)

Results

2.8s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify206.0ms (0.9%)

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

prune7.0ms (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

52.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	52.0b	(/.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

▶

52.0b

(/.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)

localize30.0ms (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)))
✓	39.0b	(/.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))
✓	44.0b	(/.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))))

series5.2s (22.7%)

Counts

4 → 144

Calls

4 calls:

4.6s	(/.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))
492.0ms	(/.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))))
46.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
17.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite100.0ms (0.4%)

Algorithm

2×	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 → 113

Calls

4 calls:

95.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
95.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
95.0ms	(/.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))
95.0ms	(/.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
0	0	0
1	0	0

simplify372.0ms (1.6%)

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

257 → 268

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2376	40163
1	5421	40163

prune1.1s (4.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	259	9	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	260	9	269

Error

11.3b

Counts

269 → 9

Alt Table

Status	Error	Program
	41.7b	(.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))))
	63.7b	(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
	55.1b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	42.4b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.8b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	52.2b	(.f64 (/.f64 (pow.f64 (cbrt.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))) 2) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (cbrt.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))))
▶	17.4b	1/16
	50.8b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 4))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	60.1b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.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 59307 to 35652 computations (39.9% saved)

localize0.0ms (0%)

prune13.0ms (0.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

11.3b

Counts

9 → 9

Alt Table

Status	Error	Program
▶	41.7b	(.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))))
	63.7b	(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
	55.1b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	42.4b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.8b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	52.2b	(.f64 (/.f64 (pow.f64 (cbrt.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))) 2) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (cbrt.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))))
✓	17.4b	1/16
	50.8b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 4))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	60.1b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.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 702 to 368 computations (47.6% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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))))
✓	35.8b	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
✓	36.2b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	40.1b	(sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))

series3.2s (13.9%)

Counts

4 → 144

Calls

4 calls:

3.0s	(.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))))
86.0ms	(sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))
62.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
41.0ms	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite57.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

229×	`add-sqr-sqrt_binary64`
219×	`log1p-expm1-u_binary64`
219×	`expm1-log1p-u_binary64`
213×	`add-cbrt-cube_binary64`
213×	`add-log-exp_binary64`

Counts

4 → 113

Calls

4 calls:

53.0ms	(.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))))
53.0ms	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
53.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
53.0ms	(sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	122
1	461	115
2	4919	115
0	0	0
1	0	0

simplify319.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

629×	`fma-def_binary64`
415×	`associate-/l*_binary64`
336×	`associate-/r*_binary64`
333×	`times-frac_binary64`
73×	`sub-neg_binary64`

Counts

257 → 303

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2320	38751
1	5266	38751

prune1.7s (7.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	385	1	386
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	388	7	395

Error

11.3b

Counts

395 → 7

Alt Table

Status	Error	Program
✓	41.7b	(.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))))
	63.7b	(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
▶	41.8b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	52.2b	(.f64 (/.f64 (pow.f64 (cbrt.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))) 2) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (cbrt.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))))
✓	17.4b	1/16
	50.8b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 4))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	57.1b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))

Compiler

Compiled 71734 to 42049 computations (41.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.3b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
✓	32.3b	(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))
	35.8b	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
	36.2b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

series4.2s (18.6%)

Counts

2 → 72

Calls

2 calls:

3.3s

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

896.0ms

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

rewrite95.0ms (0.4%)

Algorithm

2×	batch-egg-rewrite

Rules

213×	`add-sqr-sqrt_binary64`
204×	`log1p-expm1-u_binary64`
204×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`
198×	`add-log-exp_binary64`

Counts

2 → 106

Calls

2 calls:

89.0ms

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

89.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	102
1	437	95
2	4920	95
3	5041	95
0	0	0
1	0	0

simplify414.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
563×	`associate-/l*_binary64`
511×	`times-frac_binary64`
56×	`sqr-pow_binary64`
39×	`sub-neg_binary64`

Counts

178 → 202

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2723	47834
1	5594	47834

prune1.3s (5.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	320	1	321
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	321	7	328

Error

11.3b

Counts

328 → 7

Alt Table

Status	Error	Program
✓	41.7b	(.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))))
	63.7b	(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
✓	41.8b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
✓	17.4b	1/16
	50.8b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (cbrt.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 4))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	46.3b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (-.f64 (.f64 1/8 (/.f64 1 i)) (.f64 1/16 (+.f64 (/.f64 alpha (.f64 i i)) (/.f64 beta (.f64 i i))))))
	57.1b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))

Compiler

Compiled 78451 to 47377 computations (39.6% saved)

regimes1.2s (5.2%)

Accuracy

Total 2.7b remaining (21.4%)

Threshold costs 0b (0%)

Counts

173 → 2

Compiler

Compiled 35660 to 19673 computations (44.8% saved)

bsearch45.0ms (0.2%)

Steps

Iters	Range		Point
8	1.0772799134112561e+132	2.776638431680519e+134	1.4297873900624532e+134

Compiler

Compiled 4 to 3 computations (25% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	73
1	46	73
2	68	71
3	89	71
4	101	71
5	106	71
6	107	71
7	105	71

end138.0ms (0.6%)

Remove: (sort alpha beta)
Compiler: Compiled 438 to 233 computations (46.8% saved)

Details

analyze110.0ms (0.5%)

sample3.0s (13.1%)

simplify206.0ms (0.9%)

prune7.0ms (0%)

localize30.0ms (0.1%)

series5.2s (22.7%)

rewrite100.0ms (0.4%)

simplify372.0ms (1.6%)

prune1.1s (4.7%)

localize0.0ms (0%)

prune13.0ms (0.1%)

localize24.0ms (0.1%)

series3.2s (13.9%)

rewrite57.0ms (0.3%)

simplify319.0ms (1.4%)

prune1.7s (7.6%)

localize19.0ms (0.1%)

series4.2s (18.6%)

rewrite95.0ms (0.4%)

simplify414.0ms (1.8%)

prune1.3s (5.8%)

regimes1.2s (5.2%)

bsearch45.0ms (0.2%)

simplify5.0ms (0%)

end138.0ms (0.6%)

Profiling