Details

analyze52.0ms (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)

sample1.6s (13.9%)

Symmetry

(sort alpha beta)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify18.0ms (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

45.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	46.0b	(.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))))
	50.8b	(/.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))

Status

Error

Program

▶

46.0b

(*.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))))

50.8b

(/.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))

Compiler

Compiled 315 to 155 computations (50.8% saved)

localize18.0ms (0.2%)

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))
✓	4.0b	(.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))))
✓	44.7b	(/.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 (13%)

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))))
400.0ms	(/.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)))
34.0ms	(*.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))
32.0ms	(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta)))

rewrite54.0ms (0.5%)

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

Calls

4 calls:

50.0ms	(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta)))
50.0ms	(*.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))
50.0ms	(.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))))
50.0ms	(/.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)))

simplify291.0ms (2.6%)

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

prune1.4s (12.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	277	8	285

Error

8.6b

Counts

285 → 8

Alt Table

Status	Error	Program
	37.6b	(pow.f64 (cbrt.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)))))) 3)
	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	42.8b	(.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)))
▶	17.7b	1/16
	54.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta)))))
	37.3b	(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)

Compiler

Compiled 76160 to 46729 computations (38.6% saved)

localize0.0ms (0%)

prune11.0ms (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

8.6b

Counts

8 → 8

Alt Table

Status	Error	Program
	37.6b	(pow.f64 (cbrt.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)))))) 3)
▶	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	42.8b	(.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)))
✓	17.7b	1/16
	54.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))
	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta)))))
	37.3b	(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)

Compiler

Compiled 544 to 324 computations (40.4% saved)

localize20.0ms (0.2%)

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)))
✓	0.0b	(.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))
✓	4.0b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓	37.8b	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))

series1.8s (15.5%)

Counts

3 → 108

Calls

3 calls:

1.1s

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

448.0ms

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

185.0ms

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

rewrite41.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`log1p-expm1-u_binary64`
251×	`expm1-log1p-u_binary64`
250×	`add-cbrt-cube_binary64`
242×	`add-log-exp_binary64`
241×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	132
1	543	132

Stop Event

1×	node limit

Counts

3 → 50

Calls

3 calls:

39.0ms

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

39.0ms

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

simplify322.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary64`
511×	`times-frac_binary64`
9×	`cube-mult_binary64`
9×	`unpow2_binary64`
9×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3152	55872

Stop Event

1×	node limit

Counts

158 → 195

prune1.4s (12.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	268	3	271
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	271	8	279

Error

4.3b

Counts

279 → 8

Alt Table

Status	Error	Program
	37.6b	(pow.f64 (cbrt.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)))))) 3)
✓	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (+.f64 alpha (fma.f64 i 2 beta))))
✓	17.7b	1/16
	48.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (+.f64 i alpha) beta)))
▶	17.5b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
	37.3b	(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)

Compiler

Compiled 83095 to 52050 computations (37.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4)
✓	0.0b	(/.f64 1 (+.f64 alpha (fma.f64 i 2 beta)))
	0.0b	(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta)))
✓	0.2b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))

series141.0ms (1.2%)

Counts

3 → 108

Calls

3 calls:

94.0ms

(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))

23.0ms

(*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4)

23.0ms

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

rewrite32.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

182×	`add-sqr-sqrt_binary64`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`
176×	`add-cbrt-cube_binary64`
171×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	55
1	369	48

Stop Event

1×	node limit

Counts

3 → 69

Calls

3 calls:

30.0ms

(*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4)

30.0ms

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

30.0ms

(*.f64 (*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

719×	`fma-def_binary64`
658×	`times-frac_binary64`
584×	`associate-/l*_binary64`
210×	`+-commutative_binary64`
204×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	671	7582
1	2323	7410

Stop Event

1×	node limit

Counts

177 → 204

prune358.0ms (3.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	277	3	280
Fresh	0	5	5
Picked	1	0	1
Done	1	1	2
Total	279	9	288

Error

4.3b

Counts

288 → 9

Alt Table

Status	Error	Program
	18.5b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (cbrt.f64 (/.f64 1/4 (+.f64 alpha (fma.f64 i 2 beta)))) 3))
	37.3b	(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)
	37.6b	(pow.f64 (cbrt.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)))))) 3)
✓	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	17.7b	(.f64 (.f64 1/2 i) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
	37.3b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (+.f64 alpha (fma.f64 i 2 beta))))
	19.0b	(-.f64 1/16 (fma.f64 1/32 (.f64 (/.f64 beta (.f64 i i)) alpha) (.f64 1/64 (+.f64 (.f64 (/.f64 beta i) (/.f64 beta i)) (/.f64 (.f64 alpha alpha) (.f64 i i))))))
	48.9b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (+.f64 i alpha) beta)))

Compiler

Compiled 14945 to 8884 computations (40.6% saved)

regimes1.8s (15.5%)

Accuracy

Total 10.2b remaining (66.6%)

Threshold costs 0b (0%)

Counts

148 → 8

Compiler

Compiled 28248 to 17337 computations (38.6% saved)

bsearch175.0ms (1.5%)

Steps

Iters	Range		Point
6	1.6981302266858271e+261	1.3759382510623364e+262	4.960988974597858e+261
7	4.372267522288364e+227	8.52208195429673e+229	8.377992451191864e+229
8	3.3837289770240707e+190	1.083212871291203e+195	3.435789572452624e+190
7	7.894199351017176e+166	1.6194709857015558e+168	1.6033367610360856e+168
10	4.0607283439345766e+116	3.429263941342948e+129	4.1268322475984935e+116
0	2.2178930422417413e+89	2.2799278679866217e+89	2.2489104551141814e+89
7	7.082884456234682e+72	3.377913974197682e+74	7.234486167206169e+72

Compiler

Compiled 4 to 3 computations (25% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`+-commutative_binary64`
9×	`*-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	69	375
1	88	375
2	91	375
3	93	375
4	94	375

Stop Event

1×

saturated

end374.0ms (3.3%)

Compiler: Compiled 1357 to 736 computations (45.8% saved)

Details

analyze52.0ms (0.5%)

sample1.6s (13.9%)

simplify18.0ms (0.2%)

prune5.0ms (0%)

localize18.0ms (0.2%)

series1.5s (13%)

rewrite54.0ms (0.5%)

simplify291.0ms (2.6%)

prune1.4s (12.2%)

localize0.0ms (0%)

prune11.0ms (0.1%)

localize20.0ms (0.2%)

series1.8s (15.5%)

rewrite41.0ms (0.4%)

simplify322.0ms (2.8%)

prune1.4s (12.1%)

localize11.0ms (0.1%)

series141.0ms (1.2%)

rewrite32.0ms (0.3%)

simplify88.0ms (0.8%)

prune358.0ms (3.1%)

regimes1.8s (15.5%)

bsearch175.0ms (1.5%)

simplify8.0ms (0.1%)

end374.0ms (3.3%)

Profiling