Details

analyze180.0ms (1.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 43 to 28 computations (34.9% saved)

sample86.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	207×	body	128	valid
8.0ms	256×	pre	128	true
8.0ms	25×	body	1024	valid
4.0ms	17×	body	512	valid
1.0ms	5×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 78 to 51 computations (34.6% saved)

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
537×	`div-sub_binary64`
535×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	110	37
3	435	37
4	1672	37
5	2494	37
6	3358	37
7	5392	37

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

22.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	27.3b	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
▶	22.5b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

Status

Error

Program

27.3b

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

▶

22.5b

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

Compiler

Compiled 180 to 106 computations (41.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	12.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
✓	22.5b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series893.0ms (5.4%)

Counts

3 → 108

Calls

3 calls:

531.0ms

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

341.0ms

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

19.0ms

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

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 67

Calls

3 calls:

8.0ms

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

4.0ms

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

0.0ms

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

simplify201.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

561×	`+-commutative_binary64`
490×	`fma-def_binary64`
487×	`associate-+r+_binary64`
392×	`*-commutative_binary64`
294×	`associate-*r/_binary64`

Counts

175 → 205

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1400	19973
1	5450	19973

prune492.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	202	3	205
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	204	3	207

Error

0.2b

Counts

207 → 3

Alt Table

Status	Error	Program
	49.4b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	53.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)
▶	12.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)

Compiler

Compiled 24805 to 16016 computations (35.4% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	12.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series1.4s (8.5%)

Counts

3 → 108

Calls

3 calls:

1.0s

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

337.0ms

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

50.0ms

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

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
24×	`associate-/l*_binary64`

Counts

3 → 169

Calls

3 calls:

11.0ms

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

5.0ms

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

0.0ms

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

simplify278.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
477×	`associate-+r+_binary64`
326×	`associate-*r/_binary64`
177×	`associate-/l*_binary64`
171×	`associate-/r*_binary64`

Counts

277 → 297

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1591	25853
1	5046	25853

prune666.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	295	2	297
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	296	4	300

Error

0.2b

Counts

300 → 4

Alt Table

Status	Error	Program
	49.4b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	13.1b	(/.f64 (exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
▶	12.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
	53.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)

Compiler

Compiled 30461 to 18864 computations (38.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.8b	(cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))
✓	12.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 1)

series978.0ms (5.9%)

Counts

4 → 144

Calls

4 calls:

605.0ms	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
153.0ms	(/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))
152.0ms	(*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))
68.0ms	(cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
46×	`*-un-lft-identity_binary64`
37×	`cbrt-prod_binary64`
32×	`add-cube-cbrt_binary64`
30×	`times-frac_binary64`

Counts

4 → 123

Calls

4 calls:

10.0ms	(/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))
5.0ms	(*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))
1.0ms	(cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))
0.0ms	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 1)

simplify319.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

471×	`fma-def_binary64`
412×	`associate-+r+_binary64`
255×	`associate-*r/_binary64`
207×	`associate-/l*_binary64`
186×	`associate-r_binary64`

Counts

267 → 360

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1907	23600
1	5574	23600

prune1.2s (7.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	524	2	526
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	525	5	530

Error

0.2b

Counts

530 → 5

Alt Table

Status	Error	Program
	49.4b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	13.1b	(/.f64 (exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
	53.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)
	13.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 1)) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 1))) (cbrt.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 1))) 2)
▶	12.9b	(/.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))))) 1) 2)

Compiler

Compiled 54209 to 35399 computations (34.7% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(*.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))
	0.8b	(cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))
✓	1.3b	(.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))))
✓	8.2b	(+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))))) 1)

series829.0ms (5%)

Counts

2 → 72

Calls

2 calls:

527.0ms

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

302.0ms

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

rewrite958.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Rules

3237×	`times-frac_binary64`
1825×	`*-un-lft-identity_binary64`
1392×	`add-sqr-sqrt_binary64`
1007×	`add-cube-cbrt_binary64`
992×	`associate-r_binary64`

Counts

2 → 1071

Calls

2 calls:

207.0ms

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

74.0ms

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

simplify972.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

536×	`associate-*r/_binary64`
354×	`fma-def_binary64`
349×	`associate-+r+_binary64`
342×	`associate-/r/_binary64`
256×	`associate-/l*_binary64`

Counts

1143 → 1117

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1883	77139
1	5520	77139

prune4.3s (25.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1460	2	1462
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	1462	5	1467

Error

0.2b

Counts

1467 → 5

Alt Table

Status	Error	Program
	49.4b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	13.1b	(/.f64 (exp.f64 (log.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
	12.9b	(/.f64 (+.f64 (log1p.f64 (expm1.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))))))) 1) 2)
	13.0b	(/.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (/.f64 (+.f64 alpha beta) (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) 3) 1) (fma.f64 (/.f64 (/.f64 (+.f64 alpha beta) (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) (/.f64 (/.f64 (+.f64 alpha beta) (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta)))))) (-.f64 1 (/.f64 (/.f64 (+.f64 alpha beta) (.f64 (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (cbrt.f64 (fma.f64 2 i (+.f64 alpha beta))))))))) 2)
	53.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)

Compiler

Compiled 137597 to 80764 computations (41.3% saved)

regimes974.0ms (5.9%)

Accuracy

Total 1.3b remaining (90.5%)

Threshold costs 0b (0%)

Counts

94 → 2

Compiler

Compiled 27445 to 17199 computations (37.3% saved)

bsearch6.0ms (0%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-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	32	100
1	44	100
2	47	100
3	49	100
4	50	100
5	49	100

end1.0ms (0%)

Compiler: Compiled 71 to 42 computations (40.8% saved)

sample1.7s (10.1%)

Algorithm

1×

intervals

Results

500.0ms	6490×	body	128	valid
211.0ms	8000×	pre	128	true
206.0ms	665×	body	1024	valid
112.0ms	505×	body	512	valid
46.0ms	292×	body	256	valid
18.0ms	48×	body	2048	valid

Compiler

Compiled 541 to 315 computations (41.8% saved)

Details

analyze180.0ms (1.1%)

sample86.0ms (0.5%)

simplify50.0ms (0.3%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series893.0ms (5.4%)

rewrite17.0ms (0.1%)

simplify201.0ms (1.2%)

prune492.0ms (3%)

localize11.0ms (0.1%)

series1.4s (8.5%)

rewrite58.0ms (0.4%)

simplify278.0ms (1.7%)

prune666.0ms (4%)

localize19.0ms (0.1%)

series978.0ms (5.9%)

rewrite25.0ms (0.2%)

simplify319.0ms (1.9%)

prune1.2s (7.2%)

localize17.0ms (0.1%)

series829.0ms (5%)

rewrite958.0ms (5.8%)

simplify972.0ms (5.9%)

prune4.3s (25.8%)

regimes974.0ms (5.9%)

bsearch6.0ms (0%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.7s (10.1%)

Profiling