Midpoint on a great circle

Time bar (total: 5.0s)

analyze730.0ms (14.7%)

Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
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 25 to 15 computations (40% saved)

Precisions
Click to see histograms. Total time spent on operations: 449.0ms
ival-cos: 213.0ms (47.4% of total)
ival-mult: 91.0ms (20.3% of total)
ival-atan2: 41.0ms (9.1% of total)
ival-sin: 39.0ms (8.7% of total)
ival-add: 37.0ms (8.2% of total)
ival-sub: 26.0ms (5.8% of total)
const: 2.0ms (0.4% of total)

sample3.4s (68.4%)

Results
1.4s1986×1024valid
914.0ms4844×256valid
555.0ms1326×512valid
132.0ms100×2048valid
Precisions
Click to see histograms. Total time spent on operations: 2.5s
ival-cos: 1.1s (43.4% of total)
ival-atan2: 487.0ms (19.8% of total)
ival-sin: 421.0ms (17.1% of total)
ival-mult: 214.0ms (8.7% of total)
ival-add: 165.0ms (6.7% of total)
ival-sub: 93.0ms (3.8% of total)
const: 11.0ms (0.4% of total)
Bogosity

preprocess344.0ms (6.9%)

Algorithm
1×egg-herbie
Rules
823×fma-neg
781×fma-define
250×unsub-neg
209×distribute-lft-neg-in
184×sub-neg
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01031448
11791356
22941348
35841348
49911348
513491348
617441348
721221348
825841348
931511348
1038841348
1142321348
1244101348
1344991348
1445231348
1545271348
1645271348
1745921348
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)

explain442.0ms (8.9%)

FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
76106(-2.2476587330192745e+244 7.57143598198023e-43 2.1385531045468185e+97 2.206198494821928e+177)0-(sin.f64 (-.f64 lambda1 lambda2))
76106(-2.2476587330192745e+244 7.57143598198023e-43 2.1385531045468185e+97 2.206198494821928e+177)0-(cos.f64 (-.f64 lambda1 lambda2))
70-1(6.078466413723851e+270 7.808081293835102e+239 7.206343764545212e+38 2.0309476287427404e-212)(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
00-0-(cos.f64 phi2)
00-0-lambda1
00-0-(cos.f64 phi1)
00-0-(-.f64 lambda1 lambda2)
00-0-(*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))
00-0-(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
00-0-(atan2.f64 (*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
00-0-phi2
00-0-(+.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))))))
00-0-lambda2
00-0-phi1
Results
147.0ms252×256valid
101.0ms138×1024valid
75.0ms104×512valid
29.0ms18×2048valid
Compiler

Compiled 196 to 44 computations (77.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 273.0ms
ival-mult: 108.0ms (39.6% of total)
ival-cos: 79.0ms (29% of total)
ival-atan2: 43.0ms (15.8% of total)
ival-sin: 26.0ms (9.5% of total)
ival-add: 10.0ms (3.7% of total)
ival-sub: 6.0ms (2.2% of total)
const: 1.0ms (0.4% of total)

eval0.0ms (0%)

Compiler

Compiled 4 to 4 computations (0% saved)

prune1.0ms (0%)

Alt Table
Click to see full alt table
StatusAccuracyProgram
98.7%
(+.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)

simplify3.0ms (0.1%)

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)

IterNodesCost
02287
12887
23387
33587
43687
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%)

Stop Event
1×fuel
Compiler

Compiled 24 to 14 computations (41.7% saved)

preprocess49.0ms (1%)

Remove

(abs phi2)

(abs phi1)

Compiler

Compiled 288 to 168 computations (41.7% saved)

end0.0ms (0%)

Profiling

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