Details

analyze993.0ms (11.5%)

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)

sample132.0ms (1.5%)

Algorithm

1×

intervals

Symmetry

(sort a1 a2)

Results

25.0ms	54×	body	1024	valid
21.0ms	44×	body	1024	invalid
18.0ms	161×	body	128	valid
13.0ms	31×	body	512	valid
10.0ms	33×	body	512	invalid
3.0ms	15×	body	256	invalid
3.0ms	28×	body	128	invalid
2.0ms	10×	body	256	valid

Compiler

Compiled 48 to 34 computations (29.2% saved)

simplify10.0ms (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

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
	0.4b	(+.f64 (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a1 a1)) (.f64 (/.f64 (cos.f64 th) (sqrt.f64 2)) (.f64 a2 a2)))

Compiler

Compiled 108 to 70 computations (35.2% saved)

localize8.0ms (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))

series78.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

52.0ms	(.f64 (cos.f64 th) (/.f64 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 2)))
19.0ms	(/.f64 (fma.f64 a1 a1 (*.f64 a2 a2)) (sqrt.f64 2))
6.0ms	(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))

simplify100.0ms (1.2%)

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

prune164.0ms (1.9%)

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

0.0b

Counts

176 → 8

Alt Table

Status	Error	Program
	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (hypot.f64 a2 a1) (cbrt.f64 (sqrt.f64 2)))))
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
▶	0.4b	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
	0.7b	(.f64 (.f64 (cos.f64 th) (/.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 (fma.f64 a1 a1 (.f64 a2 a2)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))

Compiler

Compiled 4101 to 1917 computations (53.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))
✓	0.4b	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))

series80.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

53.0ms	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
27.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

4.0ms	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
3.0ms	(.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th))

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Rules

621×	`associate-/l*_binary64`
434×	`fma-def_binary64`
363×	`times-frac_binary64`
311×	`cancel-sign-sub-inv_binary64`
241×	`distribute-rgt-in_binary64`

Counts

121 → 108

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	158	2817
1	380	2600
2	1512	2219
3	4914	2217
4	5018	2217

prune91.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	109	7	116

Error

0.0b

Counts

116 → 7

Alt Table

Status	Error	Program
	0.6b	(.f64 (cos.f64 th) (/.f64 1 (/.f64 (sqrt.f64 2) (fma.f64 a1 a1 (.f64 a2 a2)))))
	0.5b	(/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
✓	0.4b	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (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))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))

Compiler

Compiled 2541 to 1253 computations (50.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
✓	0.4b	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
✓	6.2b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

series330.0ms (3.8%)

Counts

4 → 108

Calls

4 calls:

185.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
109.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
23.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
13.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

rewrite109.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

526×	`times-frac_binary64`
306×	`add-sqr-sqrt_binary64`
281×	`*-un-lft-identity_binary64`
281×	`add-cube-cbrt_binary64`
272×	`sqrt-prod_binary64`

Counts

4 → 401

Calls

4 calls:

28.0ms	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))))
8.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (/.f64 (sqrt.f64 2) (hypot.f64 a2 a1)))
3.0ms	(/.f64 (sqrt.f64 2) (hypot.f64 a2 a1))
1.0ms	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))

simplify334.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

609×	`fma-def_binary64`
353×	`associate-/r/_binary64`
280×	`*-commutative_binary64`
274×	`cancel-sign-sub-inv_binary64`
268×	`associate-/l*_binary64`

Counts

509 → 572

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	476	16630
1	1170	13399
2	3926	12746
3	4782	12746
4	4931	12746

prune425.0ms (4.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	568	4	572
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	572	7	579

Error

Counts

579 → 7

Alt Table

Status	Error	Program
▶	0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))))
✓	0.4b	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.4b	(.f64 (cos.f64 th) (.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 2)) (hypot.f64 a2 a1)))
	0.5b	(/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
	26.1b	(.f64 (cos.f64 th) (sqrt.f64 (/.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))))

Compiler

Compiled 18072 to 7124 computations (60.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
✓	0.3b	(/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1)))
	6.2b	(sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2)))
✓	6.5b	(sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))

series82.0ms (1%)

Counts

3 → 72

Calls

3 calls:

32.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
26.0ms	(sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))
24.0ms	(/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

179×	`times-frac_binary64`
155×	`sqrt-prod_binary64`
116×	`add-sqr-sqrt_binary64`
108×	`*-un-lft-identity_binary64`
108×	`add-cube-cbrt_binary64`

Counts

3 → 192

Calls

3 calls:

7.0ms	(/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (.f64 a1 a1)))))
2.0ms	(sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))
2.0ms	(/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1)))

simplify161.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

770×	`times-frac_binary64`
516×	`associate-/r*_binary64`
500×	`associate-/l*_binary64`
266×	`fma-def_binary64`
188×	`associate-/l/_binary64`

Counts

264 → 344

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	323	9587
1	618	7801
2	1667	7750
3	5001	7750

prune299.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	397	1	398
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	399	6	405

Error

Counts

405 → 6

Alt Table

Status	Error	Program
✓	0.4b	(.f64 (cos.f64 th) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (.f64 a2 a2))) (sqrt.f64 (/.f64 2 (fma.f64 a2 a2 (*.f64 a1 a1))))))
✓	0.4b	(/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
	0.5b	(*.f64 (cos.f64 th) (/.f64 (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2))) (/.f64 (sqrt.f64 (sqrt.f64 2)) (hypot.f64 a2 a1))))
	0.6b	(.f64 (.f64 (cos.f64 th) (/.f64 (hypot.f64 a2 a1) (sqrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (fma.f64 a1 a1 (*.f64 a2 a2))) (sqrt.f64 (sqrt.f64 2))))
	0.5b	(/.f64 (/.f64 (.f64 (fma.f64 a2 a2 (.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
	26.0b	(.f64 (cos.f64 th) (sqrt.f64 (.f64 (/.f64 (pow.f64 (hypot.f64 a1 a2) 3) 2) (hypot.f64 a1 a2))))

Compiler

Compiled 12896 to 4771 computations (63% saved)

regimes1.7s (19.2%)

Accuracy

Total 0.4b remaining (88.5%)

Threshold costs 0.4b (88.5%)

Counts

202 → 1

Compiler

Compiled 35543 to 23600 computations (33.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	12	18
2	12	18

end6.0ms (0.1%)

Remove: (sort a1 a2)
Compiler: Compiled 45 to 30 computations (33.3% saved)

sample3.4s (39.1%)

Algorithm

1×

intervals

Results

900.0ms	1856×	body	1024	valid
720.0ms	1479×	body	1024	invalid
488.0ms	4784×	body	128	valid
255.0ms	884×	body	512	valid
233.0ms	784×	body	512	invalid
107.0ms	471×	body	256	valid
83.0ms	399×	body	256	invalid
65.0ms	598×	body	128	invalid
4.0ms	5×	body	2048	valid

Compiler

Compiled 163 to 113 computations (30.7% saved)

Details

analyze993.0ms (11.5%)

sample132.0ms (1.5%)

simplify10.0ms (0.1%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series78.0ms (0.9%)

rewrite18.0ms (0.2%)

simplify100.0ms (1.2%)

prune164.0ms (1.9%)

localize8.0ms (0.1%)

series80.0ms (0.9%)

rewrite9.0ms (0.1%)

simplify85.0ms (1%)

prune91.0ms (1.1%)

localize11.0ms (0.1%)

series330.0ms (3.8%)

rewrite109.0ms (1.3%)

simplify334.0ms (3.9%)

prune425.0ms (4.9%)

localize15.0ms (0.2%)

series82.0ms (1%)

rewrite37.0ms (0.4%)

simplify161.0ms (1.9%)

prune299.0ms (3.5%)

regimes1.7s (19.2%)

simplify2.0ms (0%)

end6.0ms (0.1%)

sample3.4s (39.1%)

Profiling