Metrics for Midpoint on a great circle

analyze463.0ms (0.5%)

Memory

2.9MiB live, 178.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.8%	0.2%	0%	0%	0%	0
0%	0%	99.8%	0.2%	0%	0%	0%	1
0%	0%	99.8%	0.2%	0%	0%	0%	2
0%	0%	99.8%	0.2%	0%	0%	0%	3
0%	0%	99.8%	0.2%	0%	0%	0%	4
0%	0%	99.8%	0.2%	0%	0%	0%	5
0%	0%	99.8%	0.2%	0%	0%	0%	6
0%	0%	99.8%	0.2%	0%	0%	0%	7
0%	0%	99.8%	0.2%	0%	0%	0%	8
9.4%	9.4%	90.4%	0.2%	0%	0%	0%	9
9.4%	9.4%	90.4%	0.2%	0%	0%	0%	10
10.9%	10.9%	88.9%	0.2%	0%	0%	0%	11
10.9%	10.9%	88.9%	0.2%	0%	0%	0%	12

Compiler

Compiled 47 to 31 computations (34% saved)

sample1.5min (99.1%)

Memory

17.3MiB live, 45 558.9MiB allocated

Samples

1.7s	6 160×	0	valid-baseline
1.3s	2 084×	1	valid-baseline
1.1s	2 084×	1	valid-sollya
1.1s	6 160×	0	valid-sollya
731.0ms	2 084×	1	valid-rival
682.0ms	6 160×	0	valid-rival
6.0ms	10×	2	valid-baseline
4.0ms	10×	2	valid-rival
1.0ms	10×	2	valid-sollya
0.0ms	2×	0	valid-rival+sollya-real

Bogosity

preprocess333.0ms (0.4%)

Memory

-3.2MiB live, 43.5MiB allocated

Algorithm

1×	egg-herbie

Rules

823×	`fmm-def`
781×	`fma-define`
227×	`unsub-neg`
209×	`distribute-lft-neg-in`
185×	`sub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1448
1	179	1356
2	294	1348
3	584	1348
4	991	1348
5	1349	1348
6	1744	1348
7	2122	1348
8	2585	1348
9	3152	1348
10	3885	1348
11	4234	1348
12	4412	1348
13	4501	1348
14	4525	1348
15	4529	1348
16	4529	1348
17	4594	1348

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 (neg.f64 lambda1) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 (neg.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2)))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 (neg.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 (neg.f64 phi2)) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 (neg.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))
(neg.f64 (+.f64 (neg.f64 lambda1) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)))))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 (neg.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2))))))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 (neg.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 (neg.f64 phi2)) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 (neg.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
(+.f64 lambda2 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda2 lambda1))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))))))
(+.f64 phi1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 phi1 lambda2))) (+.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 phi1 lambda2))))))
(+.f64 phi2 (atan2.f64 (.f64 (cos.f64 lambda1) (sin.f64 (-.f64 phi2 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 lambda1) (cos.f64 (-.f64 phi2 lambda2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 phi1))) (+.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 phi1))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 lambda2) (sin.f64 (-.f64 lambda1 phi2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 lambda2) (cos.f64 (-.f64 lambda1 phi2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi1) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2))))))

Outputs
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
(+.f64 (neg.f64 lambda1) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2))))))
(-.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)) (cos.f64 phi1))) lambda1)
(-.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda2) lambda1))) (fma.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2)) (cos.f64 phi1))) lambda1)
(-.f64 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2)) (cos.f64 phi1))) lambda1)
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 (neg.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2)))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (+.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2)) (cos.f64 phi1))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 (neg.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 (neg.f64 phi2)) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 (neg.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
(neg.f64 (+.f64 (neg.f64 lambda1) (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)))))))
(-.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 (neg.f64 lambda1) lambda2)) (cos.f64 phi1))))
(-.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda2) lambda1))) (fma.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2)) (cos.f64 phi1))))
(-.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 (neg.f64 lambda1) lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2)) (cos.f64 phi1))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 (neg.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 (neg.f64 lambda2))))))))
(-.f64 (neg.f64 lambda1) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (+.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (+.f64 lambda1 lambda2)) (cos.f64 phi1))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 (neg.f64 phi1)) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(-.f64 (neg.f64 lambda1) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 (neg.f64 phi2)) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 (neg.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))))
(neg.f64 (+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))))
(-.f64 (neg.f64 lambda1) (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
(+.f64 lambda2 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda2 lambda1))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1))))))
(+.f64 lambda2 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda2 lambda1))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda2 lambda1)) (cos.f64 phi1))))
(+.f64 lambda2 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda2 lambda1))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1))))
(+.f64 phi1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 phi1 lambda2))) (+.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 phi1 lambda2))))))
(+.f64 phi1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 phi1 lambda2))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 phi1 lambda2)) (cos.f64 lambda1))))
(+.f64 phi2 (atan2.f64 (.f64 (cos.f64 lambda1) (sin.f64 (-.f64 phi2 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 lambda1) (cos.f64 (-.f64 phi2 lambda2))))))
(+.f64 phi2 (atan2.f64 (*.f64 (cos.f64 lambda1) (sin.f64 (-.f64 phi2 lambda2))) (fma.f64 (cos.f64 lambda1) (cos.f64 (-.f64 phi2 lambda2)) (cos.f64 phi1))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 phi1))) (+.f64 (cos.f64 lambda2) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 phi1))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 phi1))) (fma.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 phi1)) (cos.f64 lambda2))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 lambda2) (sin.f64 (-.f64 lambda1 phi2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 lambda2) (cos.f64 (-.f64 lambda1 phi2))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (cos.f64 lambda2) (sin.f64 (-.f64 lambda1 phi2))) (fma.f64 (cos.f64 lambda2) (cos.f64 (-.f64 lambda1 phi2)) (cos.f64 phi1))))
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi1) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (+.f64 (cos.f64 phi2) (.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2))))))
(+.f64 lambda1 (atan2.f64 (*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi1)) (fma.f64 (cos.f64 phi1) (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))))

Symmetry

(abs phi1)

(abs phi2)

Compiler

Compiled 24 to 14 computations (41.7% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 4 to 4 computations (0% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.5%	(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Compiler

Compiled 48 to 28 computations (41.7% saved)

simplify2.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
3×	`*-commutative`
2×	`sub-neg`
1×	`neg-sub0`
1×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	87
1	28	87
2	33	87
3	35	87
4	36	87

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

Outputs
(+.f64 lambda1 (atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))))

soundness0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 24 to 14 computations (41.7% saved)

preprocess28.0ms (0%)

Memory

-6.6MiB live, 27.0MiB allocated

Remove

(abs phi2)

(abs phi1)

Compiler

Compiled 288 to 168 computations (41.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze463.0ms (0.5%)

sample1.5min (99.1%)

preprocess333.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify2.0ms (0%)

soundness0.0ms (0%)

preprocess28.0ms (0%)

end0.0ms (0%)

Profiling