Details

analyze53.0ms (0.4%)

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)

sample1.5s (13%)

Symmetry

(sort alpha beta)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify20.0ms (0.2%)

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

45.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	52.1b	(/.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))
▶	45.9b	(.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

52.1b

(/.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))

▶

45.9b

(*.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
✓	0.1b	(*.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))
✓	0.3b	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))
✓	4.3b	(.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))))
✓	45.1b	(/.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)))

series1.5s (12.4%)

Counts

4 → 144

Calls

4 calls:

1.0s	(.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))))
398.0ms	(/.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)))
31.0ms	(*.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))
31.0ms	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))

rewrite48.0ms (0.4%)

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	152
1	411	137

Stop Event

1×	node limit

Counts

4 → 98

Calls

4 calls:

46.0ms	(*.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))
46.0ms	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))
46.0ms	(.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))))
46.0ms	(/.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)))

simplify296.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-def_binary64`
570×	`associate-/l*_binary64`
511×	`times-frac_binary64`
69×	`sub-neg_binary64`
56×	`sqr-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2906	51644

Stop Event

1×	node limit

Counts

242 → 276

prune1.5s (12.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	268	8	276
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	270	8	278

Error

10.7b

Counts

278 → 8

Alt Table

Status	Error	Program
	46.8b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
	53.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (-.f64 (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 alpha (.f64 beta beta))) (fma.f64 5 (/.f64 (.f64 i i) (pow.f64 beta 3)) (fma.f64 3 (/.f64 (.f64 alpha alpha) (pow.f64 beta 3)) (*.f64 8 (/.f64 i (/.f64 (pow.f64 beta 3) alpha)))))))
	38.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	38.0b	(.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))))
▶	20.5b	1/16
	48.1b	(.f64 (/.f64 i (pow.f64 (+.f64 beta (.f64 2 i)) 2)) (/.f64 (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i)) (+.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (*.f64 beta i)))) -1)))
	52.9b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	53.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))

Compiler

Compiled 75330 to 46302 computations (38.5% saved)

localize0.0ms (0%)

prune12.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

10.7b

Counts

8 → 8

Alt Table

Status	Error	Program
	46.8b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
	53.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (-.f64 (+.f64 (/.f64 i (.f64 beta beta)) (/.f64 alpha (.f64 beta beta))) (fma.f64 5 (/.f64 (.f64 i i) (pow.f64 beta 3)) (fma.f64 3 (/.f64 (.f64 alpha alpha) (pow.f64 beta 3)) (*.f64 8 (/.f64 i (/.f64 (pow.f64 beta 3) alpha)))))))
	38.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
▶	38.0b	(.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))))
✓	20.5b	1/16
	48.1b	(.f64 (/.f64 i (pow.f64 (+.f64 beta (.f64 2 i)) 2)) (/.f64 (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i)) (+.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (*.f64 beta i)))) -1)))
	52.9b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	53.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))

Compiler

Compiled 542 to 312 computations (42.4% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))
✓	4.3b	(.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))))
✓	30.8b	(/.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))
✓	33.0b	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta)))

series1.5s (12.4%)

Counts

3 → 108

Calls

3 calls:

1.0s

(*.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))))

415.0ms

(/.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))

43.0ms

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

rewrite41.0ms (0.3%)

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

Calls

3 calls:

39.0ms

(*.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))))

39.0ms

(/.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))

39.0ms

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

simplify304.0ms (2.6%)

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

prune1.4s (12.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	261	8	269

Error

10.7b

Counts

269 → 8

Alt Table

Status	Error	Program
	46.8b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
▶	38.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓	38.0b	(.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))))
✓	20.5b	1/16
	53.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (-.f64 (+.f64 i alpha) (+.f64 (/.f64 (pow.f64 alpha 2) beta) (+.f64 (/.f64 (pow.f64 i 2) beta) (.f64 2 (/.f64 (*.f64 i alpha) beta))))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	48.1b	(.f64 (/.f64 i (pow.f64 (+.f64 beta (.f64 2 i)) 2)) (/.f64 (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i)) (+.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (*.f64 beta i)))) -1)))
	52.9b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	53.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))

Compiler

Compiled 75651 to 47137 computations (37.7% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	14.0b	(.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))
✓	16.4b	(/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))
✓	17.1b	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta)))
✓	33.9b	(cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)))

series1.1s (9.2%)

Counts

4 → 72

Calls

4 calls:

445.0ms	(.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))
303.0ms	(/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))
298.0ms	(/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta)))
40.0ms	(cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)))

rewrite56.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

218×	`add-sqr-sqrt_binary64`
211×	`log1p-expm1-u_binary64`
211×	`expm1-log1p-u_binary64`
210×	`add-cbrt-cube_binary64`
203×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	117
1	436	117

Stop Event

1×	node limit

Counts

4 → 111

Calls

4 calls:

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

simplify224.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

601×	`fma-def_binary64`
335×	`associate-/l*_binary64`
271×	`associate-*r/_binary64`
192×	`associate-/r*_binary64`
178×	`times-frac_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2284	38194

Stop Event

1×	node limit

Counts

183 → 230

prune1.1s (9.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	273	2	275
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	274	9	283

Error

10.7b

Counts

283 → 9

Alt Table

Status	Error	Program
✓	20.5b	1/16
	38.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (.f64 (/.f64 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) 1) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (+.f64 alpha (fma.f64 i 2 beta)))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	53.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 1 (/.f64 (-.f64 (+.f64 i alpha) (+.f64 (/.f64 (pow.f64 alpha 2) beta) (+.f64 (/.f64 (pow.f64 i 2) beta) (.f64 2 (/.f64 (*.f64 i alpha) beta))))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	48.6b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 alpha (fma.f64 i 2 beta))) (.f64 (pow.f64 (+.f64 (.f64 i alpha) (pow.f64 i 2)) 1/3) (/.f64 1 (-.f64 (+.f64 (.f64 4 (.f64 i alpha)) (+.f64 (pow.f64 alpha 2) (*.f64 4 (pow.f64 i 2)))) 1)))))
	46.8b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
✓	38.0b	(.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))))
	48.1b	(.f64 (/.f64 i (pow.f64 (+.f64 beta (.f64 2 i)) 2)) (/.f64 (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i)) (+.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (*.f64 beta i)))) -1)))
	52.9b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	53.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))

Compiler

Compiled 64868 to 37271 computations (42.5% saved)

regimes775.0ms (6.5%)

Accuracy

Total 2.7b remaining (21.7%)

Threshold costs 0b (0%)

Counts

78 → 2

Compiler

Compiled 21128 to 12545 computations (40.6% saved)

bsearch33.0ms (0.3%)

Steps

Iters	Range		Point
7	5.383573744591192e+118	9.247192847421891e+119	5.448163523978264e+118

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	68
1	45	68

Stop Event

1×

saturated

end328.0ms (2.8%)

Compiler: Compiled 550 to 330 computations (40% saved)

Details

analyze53.0ms (0.4%)

sample1.5s (13%)

simplify20.0ms (0.2%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series1.5s (12.4%)

rewrite48.0ms (0.4%)

simplify296.0ms (2.5%)

prune1.5s (12.3%)

localize0.0ms (0%)

prune12.0ms (0.1%)

localize24.0ms (0.2%)

series1.5s (12.4%)

rewrite41.0ms (0.3%)

simplify304.0ms (2.6%)

prune1.4s (12.1%)

localize27.0ms (0.2%)

series1.1s (9.2%)

rewrite56.0ms (0.5%)

simplify224.0ms (1.9%)

prune1.1s (9.5%)

regimes775.0ms (6.5%)

bsearch33.0ms (0.3%)

simplify2.0ms (0%)

end328.0ms (2.8%)

Profiling