Details

analyze1.1s (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 23 to 16 computations (30.4% saved)

sample4.6s (40.5%)

Symmetry

(sort a1 a2)

Results

1.2s	1814×	body	1024	valid
1.1s	1580×	body	1024	invalid
1.1s	5081×	body	128	valid
384.0ms	868×	body	512	valid
347.0ms	805×	body	512	invalid
157.0ms	486×	body	256	valid
151.0ms	398×	body	256	invalid
111.0ms	647×	body	128	invalid
9.0ms	7×	body	2048	valid

Compiler

Compiled 68 to 47 computations (30.9% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
23×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
11×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	27	18
2	53	18
3	76	18
4	103	18
5	117	18
6	132	18
7	134	18
8	136	18
9	136	18

prune4.0ms (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

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.5b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))
▶	0.5b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
✓	0.4b	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))

series83.0ms (0.7%)

Counts

3 → 84

Calls

3 calls:

54.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
22.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
7.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
22×	`associate-r_binary64`

Counts

3 → 95

Calls

3 calls:

7.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
3.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
0.0ms	(fma.f64 a1 a1 (*.f64 a2 a2))

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-l_binary64`
410×	`associate-r_binary64`
396×	`fma-neg_binary64`
332×	`associate-/l*_binary64`
299×	`sub-neg_binary64`

Counts

179 → 174

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	3607
1	368	3275
2	1296	3231
3	4370	3231
4	5109	3231

prune177.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	166	8	174
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	168	8	176

Error

Counts

176 → 8

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.8b	(.f64 (.f64 (cbrt.f64 (cos.f64 th)) (cbrt.f64 (cos.f64 th))) (.f64 (cbrt.f64 (cos.f64 th)) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2))))
	0.7b	(.f64 (cos.f64 th) (.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 2))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))

Compiler

Compiled 4117 to 1921 computations (53.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
✓	0.5b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
✓	4.8b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series267.0ms (2.3%)

Counts

4 → 120

Calls

4 calls:

190.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
34.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
24.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
18.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`sqrt-prod_binary64`
72×	`times-frac_binary64`
65×	`add-sqr-sqrt_binary64`
60×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`

Counts

4 → 162

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2)))
4.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 2))
3.0ms	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify212.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

621×	`fma-def_binary64`
376×	`cancel-sign-sub-inv_binary64`
345×	`associate-l_binary64`
317×	`sub-neg_binary64`
308×	`fma-neg_binary64`

Counts

282 → 332

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	347	7564
1	936	6108
2	3364	6008
3	4799	6003
4	4932	6003
5	5038	6003

prune268.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	329	3	332
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	333	7	340

Error

Counts

340 → 7

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))))
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))

Compiler

Compiled 9384 to 4006 computations (57.3% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 a1 a1 (*.f64 a2 a2))
	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
✓	4.9b	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

series145.0ms (1.3%)

Counts

2 → 60

Calls

2 calls:

124.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
20.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-prod_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 61

Calls

2 calls:

7.0ms	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2)))
4.0ms	(sqrt.f64 (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) 2))

simplify120.0ms (1%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
617×	`fma-neg_binary64`
484×	`cancel-sign-sub-inv_binary64`
288×	`associate-r_binary64`
252×	`associate-l_binary64`

Counts

121 → 153

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	4340
1	704	3830
2	2584	3142
3	4948	3142
4	5234	3142

prune227.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	242	2	244
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	245	6	251

Error

Counts

251 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 (/.f64 1 2)))
▶	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 6963 to 3222 computations (53.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))
	0.1b	(*.f64 (cos.f64 th) (hypot.f64 a2 a1))
✓	0.3b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))))
✓	0.3b	(*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2)))

series148.0ms (1.3%)

Counts

3 → 68

Calls

3 calls:

99.0ms

(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))))

29.0ms

(sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))

19.0ms

(*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2)))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
36×	`sqrt-prod_binary64`
22×	`times-frac_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 99

Calls

3 calls:

9.0ms

(*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2)))

8.0ms

(*.f64 (*.f64 (cos.f64 th) (hypot.f64 a2 a1)) (*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))))

3.0ms

(sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))

simplify125.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-def_binary64`
497×	`cancel-sign-sub-inv_binary64`
423×	`fma-neg_binary64`
326×	`associate-r_binary64`
320×	`times-frac_binary64`

Counts

167 → 179

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	4322
1	716	3865
2	2465	3847
3	4873	3847
4	5031	3847

prune219.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	247	6	253

Error

Counts

253 → 6

Alt Table

Status	Error	Program
	0.5b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (/.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (fma.f64 a2 a2 (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 (/.f64 1 2)))
✓	0.4b	(.f64 (.f64 (cos.f64 th) (hypot.f64 a2 a1)) (*.f64 (sqrt.f64 (hypot.f64 a2 a1)) (sqrt.f64 (/.f64 (hypot.f64 a2 a1) 2))))
	0.5b	(.f64 (/.f64 (cos.f64 th) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (cbrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (cos.f64 th) (/.f64 (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))

Compiler

Compiled 7204 to 3342 computations (53.6% saved)

regimes3.1s (27.5%)

Accuracy

Total 0.3b remaining (94.5%)

Threshold costs 0.3b (94.5%)

Counts

305 → 1

Compiler

Compiled 53170 to 35348 computations (33.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	20	24
2	19	24

end265.0ms (2.3%)

Compiler: Compiled 212 to 147 computations (30.7% saved)

Details

analyze1.1s (9.8%)

sample4.6s (40.5%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series83.0ms (0.7%)

rewrite18.0ms (0.2%)

simplify113.0ms (1%)

prune177.0ms (1.6%)

localize13.0ms (0.1%)

series267.0ms (2.3%)

rewrite35.0ms (0.3%)

simplify212.0ms (1.9%)

prune268.0ms (2.3%)

localize19.0ms (0.2%)

series145.0ms (1.3%)

rewrite16.0ms (0.1%)

simplify120.0ms (1%)

prune227.0ms (2%)

localize11.0ms (0.1%)

series148.0ms (1.3%)

rewrite28.0ms (0.2%)

simplify125.0ms (1.1%)

prune219.0ms (1.9%)

regimes3.1s (27.5%)

simplify2.0ms (0%)

end265.0ms (2.3%)

Profiling