Details

analyze174.0ms (1.7%)

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)

sample2.1s (21.2%)

Results

1.1s	6727×	body	128	valid
395.0ms	507×	body	512	valid
370.0ms	666×	body	1024	valid
109.0ms	46×	body	2048	valid
104.0ms	310×	body	256	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify71.0ms (0.7%)

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

19.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.5b	(/.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)
▶	19.2b	(/.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)

Status

Error

Program

23.5b

(/.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)

▶

19.2b

(/.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)

Compiler

Compiled 180 to 106 computations (41.1% saved)

localize11.0ms (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))))
✓	12.1b	(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)
✓	16.0b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series831.0ms (8.3%)

Counts

3 → 108

Calls

3 calls:

515.0ms

(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)

286.0ms

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

29.0ms

(*.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)

simplify186.0ms (1.9%)

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

prune474.0ms (4.8%)

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

0.0b

Counts

207 → 4

Alt Table

Status	Error	Program
	50.0b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	12.1b	(/.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)
	43.7b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
	51.9b	(/.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)

Compiler

Compiled 24705 to 15946 computations (35.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.3b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	12.1b	(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)

series905.0ms (9.1%)

Counts

3 → 108

Calls

3 calls:

497.0ms

(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)

332.0ms

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

75.0ms

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

rewrite46.0ms (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:

15.0ms

(/.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 (2.8%)

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

prune1.1s (10.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	299	3	302

Error

0.0b

Counts

302 → 3

Alt Table

Status	Error	Program
	50.0b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	11.8b	(/.f64 (+.f64 (*.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)
	51.9b	(/.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)

Compiler

Compiled 30217 to 18707 computations (38.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
	0.3b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	2.2b	(*.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)))))
✓	2.6b	(+.f64 (*.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)

series825.0ms (8.3%)

Counts

2 → 72

Calls

2 calls:

503.0ms

(+.f64 (*.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)

321.0ms

(*.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)))))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`times-frac_binary64`
123×	`*-un-lft-identity_binary64`
92×	`add-sqr-sqrt_binary64`
82×	`associate-r_binary64`
59×	`add-cube-cbrt_binary64`

Counts

2 → 125

Calls

2 calls:

24.0ms

(*.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)))))

14.0ms

(+.f64 (*.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)

simplify338.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

404×	`+-commutative_binary64`
361×	`*-commutative_binary64`
354×	`fma-def_binary64`
349×	`associate-+r+_binary64`
271×	`associate-*r/_binary64`

Counts

197 → 265

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1236	21338
1	4728	21233
2	5013	21233

prune909.0ms (9.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	507	0	507
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	507	3	510

Error

0.0b

Counts

510 → 3

Alt Table

Status	Error	Program
▶	50.0b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	11.8b	(/.f64 (+.f64 (*.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)
	51.9b	(/.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)

Compiler

Compiled 48576 to 29742 computations (38.8% saved)

localize7.0ms (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)

series18.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

18.0ms

(/.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 (0.8%)

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

prune49.0ms (0.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	59	5	64

Error

0.0b

Counts

64 → 5

Alt Table

Status	Error	Program
✓	50.0b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	50.2b	(/.f64 (*.f64 (sqrt.f64 (/.f64 (fma.f64 2 beta (fma.f64 4 i 2)) alpha)) (sqrt.f64 (/.f64 (fma.f64 2 beta (fma.f64 4 i 2)) alpha))) 2)
✓	11.8b	(/.f64 (+.f64 (*.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)
	50.2b	(/.f64 (/.f64 (/.f64 (fma.f64 2 beta (fma.f64 4 i 2)) (sqrt.f64 alpha)) (sqrt.f64 alpha)) 2)
	51.9b	(/.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)

Compiler

Compiled 1369 to 978 computations (28.6% saved)

regimes1.4s (13.6%)

Accuracy

Total 1.4b remaining (92.8%)

Threshold costs 0b (0%)

Counts

108 → 2

Compiler

Compiled 19926 to 14003 computations (29.7% saved)

bsearch4.0ms (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	31	99
1	43	99
2	47	99
3	49	99
4	50	99
5	49	99

end118.0ms (1.2%)

Compiler: Compiled 298 to 182 computations (38.9% saved)

Details

analyze174.0ms (1.7%)

sample2.1s (21.2%)

simplify71.0ms (0.7%)

prune5.0ms (0%)

localize11.0ms (0.1%)

series831.0ms (8.3%)

rewrite17.0ms (0.2%)

simplify186.0ms (1.9%)

prune474.0ms (4.8%)

localize12.0ms (0.1%)

series905.0ms (9.1%)

rewrite46.0ms (0.5%)

simplify278.0ms (2.8%)

prune1.1s (10.5%)

localize11.0ms (0.1%)

series825.0ms (8.3%)

rewrite63.0ms (0.6%)

simplify338.0ms (3.4%)

prune909.0ms (9.1%)

localize7.0ms (0.1%)

series18.0ms (0.2%)

rewrite4.0ms (0%)

simplify82.0ms (0.8%)

prune49.0ms (0.5%)

regimes1.4s (13.6%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end118.0ms (1.2%)

Profiling