Details

analyze161.0ms (2%)

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)

sample2.0s (25.6%)

Results

1.3s	6650×	body	128	valid
371.0ms	727×	body	1024	valid
216.0ms	543×	body	512	valid
77.0ms	290×	body	256	valid
29.0ms	46×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify47.0ms (0.6%)

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 (0.1%)

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

22.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	22.2b	(/.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)
	28.5b	(/.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)

Status

Error

Program

▶

22.2b

(/.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)

28.5b

(/.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)

Compiler

Compiled 180 to 106 computations (41.1% saved)

localize14.0ms (0.2%)

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))))
✓	13.9b	(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)
✓	19.5b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series444.0ms (5.6%)

Counts

3 → 108

Calls

3 calls:

275.0ms

(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)

151.0ms

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

17.0ms

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

rewrite17.0ms (0.2%)

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:

7.0ms

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

6.0ms

(*.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)

simplify195.0ms (2.4%)

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

prune486.0ms (6.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	203	4	207

Error

Counts

207 → 4

Alt Table

Status	Error	Program
	50.9b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i 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)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
	13.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
	48.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	13.9b	(/.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 24693 to 15942 computations (35.4% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	13.9b	(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)

series906.0ms (11.4%)

Counts

3 → 108

Calls

3 calls:

585.0ms

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

273.0ms

(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)

48.0ms

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

rewrite40.0ms (0.5%)

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:

10.0ms

(/.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)

simplify268.0ms (3.4%)

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 → 298

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1591	25853
1	5046	25853

prune628.0ms (7.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	298	4	302

Error

Counts

302 → 4

Alt Table

Status	Error	Program
	50.9b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i 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)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
▶	13.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
	48.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	13.9b	(/.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 30248 to 18726 computations (38.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓	13.9b	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series487.0ms (6.1%)

Counts

4 → 144

Calls

4 calls:

250.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
149.0ms	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
59.0ms	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
27.0ms	(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))

rewrite44.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
65×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 162

Calls

4 calls:

19.0ms	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
6.0ms	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
2.0ms	(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
0.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify280.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-def_binary64`
560×	`associate-+r+_binary64`
386×	`associate-*r/_binary64`
174×	`associate-/l*_binary64`
155×	`associate-/r*_binary64`

Counts

306 → 370

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1717	26289
1	5484	26289

prune686.0ms (8.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	370	0	370
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	370	4	374

Error

Counts

374 → 4

Alt Table

Status	Error	Program
	50.9b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i 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)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
✓	13.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
▶	48.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	13.9b	(/.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 34458 to 21641 computations (37.2% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series16.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

16.0ms

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

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

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

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

726×	`distribute-rgt-in_binary64`
711×	`distribute-lft-in_binary64`
389×	`fma-def_binary64`
352×	`associate-/r/_binary64`
323×	`div-sub_binary64`

Counts

65 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	1277
1	132	1117
2	332	1081
3	934	1079
4	4676	1025
5	4834	1025
6	5397	1025

prune40.0ms (0.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	61	4	65

Error

Counts

65 → 4

Alt Table

Status	Error	Program
✓	13.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
✓	48.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	48.0b	(/.f64 (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 2 (/.f64 beta alpha)) (*.f64 4 (/.f64 i alpha)))) 2)
✓	13.9b	(/.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 1310 to 943 computations (28% saved)

regimes927.0ms (11.6%)

Accuracy

Total 1.3b remaining (86.3%)

Threshold costs 0b (0%)

Counts

75 → 2

Compiler

Compiled 12998 to 9069 computations (30.2% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-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	30	97
1	40	97
2	43	97
3	45	97
4	46	97
5	45	97

end102.0ms (1.3%)

Compiler: Compiled 237 to 145 computations (38.8% saved)

Details

analyze161.0ms (2%)

sample2.0s (25.6%)

simplify47.0ms (0.6%)

prune5.0ms (0.1%)

localize14.0ms (0.2%)

series444.0ms (5.6%)

rewrite17.0ms (0.2%)

simplify195.0ms (2.4%)

prune486.0ms (6.1%)

localize13.0ms (0.2%)

series906.0ms (11.4%)

rewrite40.0ms (0.5%)

simplify268.0ms (3.4%)

prune628.0ms (7.9%)

localize14.0ms (0.2%)

series487.0ms (6.1%)

rewrite44.0ms (0.6%)

simplify280.0ms (3.5%)

prune686.0ms (8.6%)

localize9.0ms (0.1%)

series16.0ms (0.2%)

rewrite4.0ms (0%)

simplify82.0ms (1%)

prune40.0ms (0.5%)

regimes927.0ms (11.6%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end102.0ms (1.3%)

Profiling