Metrics for Spherical law of cosines

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze807.0ms (16.2%)

Memory

-22.2MiB live, 903.3MiB allocated; 155ms collecting garbage

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
0%	0%	99.8%	0.2%	0%	0%	0%	9
0%	0%	99.8%	0.2%	0%	0%	0%	10
1.6%	1.6%	98.2%	0.2%	0%	0%	0%	11
1.6%	1.6%	98.2%	0.2%	0%	0%	0%	12

Compiler

Compiled 21 to 19 computations (9.5% saved)

sample3.7s (75.3%)

Memory

65.2MiB live, 3 841.7MiB allocated; 460ms collecting garbage

Samples

2.8s	6 300×	1	valid
377.0ms	1 800×	0	valid
60.0ms	125×	2	valid
39.0ms	31×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 2.9s

ival-cos: 1.2s (40.5% of total)

ival-sin: 753.0ms (26.3% of total)

adjust: 295.0ms (10.3% of total)

ival-mult!: 295.0ms (10.3% of total)

ival-acos: 282.0ms (9.9% of total)

ival-sub!: 47.0ms (1.6% of total)

ival-add!: 32.0ms (1.1% of total)

Bogosity

explain334.0ms (6.7%)

Memory

-4.9MiB live, 366.7MiB allocated; 30ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
68	137	(-54328490299.04313 -5.919569419080663e+208 1.5949777631253567e-144 1.09456024263632e-104 3.788810447627902e+32)	-	`(cos.f64 (-.f64 lambda1 lambda2))`
17	0	-	-	`(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))`
0	0	-	-	`lambda2`
0	0	-	-	`phi2`
0	0	-	-	`(*.f64 (cos.f64 phi1) (cos.f64 phi2))`
0	0	-	-	`(-.f64 lambda1 lambda2)`
0	0	-	-	`R`
0	0	-	-	`(sin.f64 phi1)`
0	0	-	-	`(cos.f64 phi2)`
0	0	-	-	`lambda1`
0	0	-	-	`(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))`
0	0	-	-	`(*.f64 (sin.f64 phi1) (sin.f64 phi2))`
0	0	-	-	`phi1`
0	0	-	-	`(sin.f64 phi2)`
0	0	-	-	`(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)`
0	0	-	-	`(+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))`
0	0	-	-	`(cos.f64 phi1)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`cos.f64`	`(cos.f64 (-.f64 lambda1 lambda2))`	sensitivity	205	0
`acos.f64`	`(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))`	sensitivity	17	3

Confusion

	Predicted +	Predicted -
+	85	1
-	137	33

Precision

0.38288288288288286

Recall

0.9883720930232558

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	85	1	0
-	137	0	33

Precision?

0.38565022421524664

Recall?

1.0

Freqs

test

number	freq
0	34
1	222

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

190.0ms	424×	1	valid
16.0ms	76×	0	valid
5.0ms	10×	2	valid
3.0ms	2×	3	valid

Compiler

Compiled 207 to 55 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 178.0ms

ival-cos: 74.0ms (41.7% of total)

ival-sin: 42.0ms (23.7% of total)

ival-mult!: 19.0ms (10.7% of total)

adjust: 18.0ms (10.1% of total)

ival-acos: 18.0ms (10.1% of total)

ival-sub!: 3.0ms (1.7% of total)

ival-add!: 2.0ms (1.1% of total)

preprocess42.0ms (0.8%)

Memory

-9.9MiB live, 35.1MiB allocated; 5ms collecting garbage

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	130	412
1	346	408
2	745	408
3	1755	408
4	3841	408

Stop Event

1×	node-limit

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	73.9%	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)

Symmetry

(negabs R)

(sort phi1 phi2)

Compiler

Compiled 38 to 34 computations (10.5% saved)

series39.0ms (0.8%)

Memory

3.3MiB live, 48.6MiB allocated; 4ms collecting garbage

Counts

17 → 106

Calls

Call 1

Inputs
(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
(+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
(*.f64 (sin.f64 phi1) (sin.f64 phi2))
(sin.f64 phi1)
phi1
(sin.f64 phi2)
phi2
(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
(*.f64 (cos.f64 phi1) (cos.f64 phi2))
(cos.f64 phi1)
(cos.f64 phi2)
(cos.f64 (-.f64 lambda1 lambda2))
(-.f64 lambda1 lambda2)
lambda1
lambda2
R

Outputs
#s(approx (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) #s(hole binary64 (* R (acos (+ (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2)))))))
#s(approx R #s(hole binary64 R))
#s(approx (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) #s(hole binary64 (acos (+ (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))) (* (sin phi1) (sin phi2)))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* -1 (* lambda1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2)))))) (+ (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))) (* (sin phi1) (sin phi2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* lambda1 (+ (* -1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2))))) (* -1/2 (* lambda1 (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))))))) (+ (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))) (* (sin phi1) (sin phi2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* lambda1 (+ (* -1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2))))) (* lambda1 (+ (* -1/2 (* (cos phi1) (* (cos phi2) (cos (neg lambda2))))) (* 1/6 (* lambda1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2)))))))))) (+ (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))) (* (sin phi1) (sin phi2))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (* (cos phi1) (* (cos phi2) (cos (neg lambda2))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* -1 (* lambda1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2)))))) (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* lambda1 (+ (* -1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2))))) (* -1/2 (* lambda1 (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))))))) (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* lambda1 (+ (* -1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2))))) (* lambda1 (+ (* -1/2 (* (cos phi1) (* (cos phi2) (cos (neg lambda2))))) (* 1/6 (* lambda1 (* (cos phi1) (* (cos phi2) (sin (neg lambda2)))))))))) (* (cos phi1) (* (cos phi2) (cos (neg lambda2)))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (cos (neg lambda2))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (+ (cos (neg lambda2)) (* -1 (* lambda1 (sin (neg lambda2)))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (+ (cos (neg lambda2)) (* lambda1 (- (* -1/2 (* lambda1 (cos (neg lambda2)))) (sin (neg lambda2)))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (+ (cos (neg lambda2)) (* lambda1 (- (* lambda1 (+ (* -1/2 (cos (neg lambda2))) (* 1/6 (* lambda1 (sin (neg lambda2)))))) (sin (neg lambda2)))))))
#s(approx (- lambda1 lambda2) #s(hole binary64 (* -1 lambda2)))
#s(approx (- lambda1 lambda2) #s(hole binary64 (- lambda1 lambda2)))
#s(approx lambda1 #s(hole binary64 lambda1))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2)))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (* (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (cos (- lambda1 lambda2))))
#s(approx (- lambda1 lambda2) #s(hole binary64 lambda1))
#s(approx (- lambda1 lambda2) #s(hole binary64 (* lambda1 (+ 1 (* -1 (/ lambda2 lambda1))))))
#s(approx (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) #s(hole binary64 (* R (acos (+ (* (cos phi1) (* (cos phi2) (cos (neg (+ lambda2 (* -1 lambda1)))))) (* (sin phi1) (sin phi2)))))))
#s(approx (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) #s(hole binary64 (acos (+ (* (cos phi1) (* (cos phi2) (cos (neg (+ lambda2 (* -1 lambda1)))))) (* (sin phi1) (sin phi2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* (cos phi1) (* (cos phi2) (cos (neg (+ lambda2 (* -1 lambda1)))))) (* (sin phi1) (sin phi2)))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (* (cos phi1) (* (cos phi2) (cos (neg (+ lambda2 (* -1 lambda1))))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (cos (neg (+ lambda2 (* -1 lambda1))))))
#s(approx (- lambda1 lambda2) #s(hole binary64 (* -1 (* lambda1 (- (/ lambda2 lambda1) 1)))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* (cos lambda1) (* (cos phi1) (cos phi2))) (* (sin phi1) (sin phi2)))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* lambda2 (* (cos phi1) (* (cos phi2) (sin lambda1)))) (+ (* (cos lambda1) (* (cos phi1) (cos phi2))) (* (sin phi1) (sin phi2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* lambda2 (+ (* -1/2 (* lambda2 (* (cos lambda1) (* (cos phi1) (cos phi2))))) (* (cos phi1) (* (cos phi2) (sin lambda1))))) (+ (* (cos lambda1) (* (cos phi1) (cos phi2))) (* (sin phi1) (sin phi2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* lambda2 (+ (* lambda2 (+ (* -1/2 (* (cos lambda1) (* (cos phi1) (cos phi2)))) (* -1/6 (* lambda2 (* (cos phi1) (* (cos phi2) (sin lambda1))))))) (* (cos phi1) (* (cos phi2) (sin lambda1))))) (+ (* (cos lambda1) (* (cos phi1) (cos phi2))) (* (sin phi1) (sin phi2))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (* (cos lambda1) (* (cos phi1) (cos phi2)))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* lambda2 (* (cos phi1) (* (cos phi2) (sin lambda1)))) (* (cos lambda1) (* (cos phi1) (cos phi2))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* lambda2 (+ (* -1/2 (* lambda2 (* (cos lambda1) (* (cos phi1) (cos phi2))))) (* (cos phi1) (* (cos phi2) (sin lambda1))))) (* (cos lambda1) (* (cos phi1) (cos phi2))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* lambda2 (+ (* lambda2 (+ (* -1/2 (* (cos lambda1) (* (cos phi1) (cos phi2)))) (* -1/6 (* lambda2 (* (cos phi1) (* (cos phi2) (sin lambda1))))))) (* (cos phi1) (* (cos phi2) (sin lambda1))))) (* (cos lambda1) (* (cos phi1) (cos phi2))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (cos lambda1)))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (+ (cos lambda1) (* lambda2 (sin lambda1)))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (+ (cos lambda1) (* lambda2 (- (* -1/2 (* lambda2 (cos lambda1))) (* -1 (sin lambda1)))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (+ (cos lambda1) (* lambda2 (- (* lambda2 (+ (* -1/2 (cos lambda1)) (* -1/6 (* lambda2 (sin lambda1))))) (* -1 (sin lambda1)))))))
#s(approx (- lambda1 lambda2) #s(hole binary64 (+ lambda1 (* -1 lambda2))))
#s(approx lambda2 #s(hole binary64 lambda2))
#s(approx (- lambda1 lambda2) #s(hole binary64 (* lambda2 (- (/ lambda1 lambda2) 1))))
#s(approx (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) #s(hole binary64 (* R (acos (+ (* (cos phi1) (* (cos phi2) (cos (+ lambda1 (* -1 lambda2))))) (* (sin phi1) (sin phi2)))))))
#s(approx (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) #s(hole binary64 (acos (+ (* (cos phi1) (* (cos phi2) (cos (+ lambda1 (* -1 lambda2))))) (* (sin phi1) (sin phi2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* (cos phi1) (* (cos phi2) (cos (+ lambda1 (* -1 lambda2))))) (* (sin phi1) (sin phi2)))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (* (cos phi1) (* (cos phi2) (cos (+ lambda1 (* -1 lambda2)))))))
#s(approx (cos (- lambda1 lambda2)) #s(hole binary64 (cos (+ lambda1 (* -1 lambda2)))))
#s(approx (- lambda1 lambda2) #s(hole binary64 (* -1 (* lambda2 (+ 1 (* -1 (/ lambda1 lambda2)))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (* (cos phi2) (cos (- lambda1 lambda2)))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* phi1 (sin phi2)) (* (cos phi2) (cos (- lambda1 lambda2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* phi1 (+ (sin phi2) (* -1/2 (* phi1 (* (cos phi2) (cos (- lambda1 lambda2))))))) (* (cos phi2) (cos (- lambda1 lambda2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* phi1 (+ (sin phi2) (* phi1 (+ (* -1/2 (* (cos phi2) (cos (- lambda1 lambda2)))) (* -1/6 (* phi1 (sin phi2))))))) (* (cos phi2) (cos (- lambda1 lambda2))))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi1 (sin phi2))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi1 (+ (sin phi2) (* -1/6 (* (pow phi1 2) (sin phi2)))))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi1 (+ (sin phi2) (* (pow phi1 2) (+ (* -1/6 (sin phi2)) (* 1/120 (* (pow phi1 2) (sin phi2)))))))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi1 (+ (sin phi2) (* (pow phi1 2) (+ (* -1/6 (sin phi2)) (* (pow phi1 2) (+ (* -1/5040 (* (pow phi1 2) (sin phi2))) (* 1/120 (sin phi2))))))))))
#s(approx (sin phi1) #s(hole binary64 phi1))
#s(approx (sin phi1) #s(hole binary64 (* phi1 (+ 1 (* -1/6 (pow phi1 2))))))
#s(approx (sin phi1) #s(hole binary64 (* phi1 (+ 1 (* (pow phi1 2) (- (* 1/120 (pow phi1 2)) 1/6))))))
#s(approx (sin phi1) #s(hole binary64 (* phi1 (+ 1 (* (pow phi1 2) (- (* (pow phi1 2) (+ 1/120 (* -1/5040 (pow phi1 2)))) 1/6))))))
#s(approx phi1 #s(hole binary64 phi1))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (* (cos phi2) (cos (- lambda1 lambda2)))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* -1/2 (* (pow phi1 2) (* (cos phi2) (cos (- lambda1 lambda2))))) (* (cos phi2) (cos (- lambda1 lambda2))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* (cos phi2) (cos (- lambda1 lambda2))) (* (pow phi1 2) (+ (* -1/2 (* (cos phi2) (cos (- lambda1 lambda2)))) (* 1/24 (* (pow phi1 2) (* (cos phi2) (cos (- lambda1 lambda2))))))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* (cos phi2) (cos (- lambda1 lambda2))) (* (pow phi1 2) (+ (* -1/2 (* (cos phi2) (cos (- lambda1 lambda2)))) (* (pow phi1 2) (+ (* -1/720 (* (pow phi1 2) (* (cos phi2) (cos (- lambda1 lambda2))))) (* 1/24 (* (cos phi2) (cos (- lambda1 lambda2)))))))))))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (cos phi2)))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (+ (cos phi2) (* -1/2 (* (pow phi1 2) (cos phi2))))))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (+ (cos phi2) (* (pow phi1 2) (+ (* -1/2 (cos phi2)) (* 1/24 (* (pow phi1 2) (cos phi2))))))))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (+ (cos phi2) (* (pow phi1 2) (+ (* -1/2 (cos phi2)) (* (pow phi1 2) (+ (* -1/720 (* (pow phi1 2) (cos phi2))) (* 1/24 (cos phi2)))))))))
#s(approx (cos phi1) #s(hole binary64 1))
#s(approx (cos phi1) #s(hole binary64 (+ 1 (* -1/2 (pow phi1 2)))))
#s(approx (cos phi1) #s(hole binary64 (+ 1 (* (pow phi1 2) (- (* 1/24 (pow phi1 2)) 1/2)))))
#s(approx (cos phi1) #s(hole binary64 (+ 1 (* (pow phi1 2) (- (* (pow phi1 2) (+ 1/24 (* -1/720 (pow phi1 2)))) 1/2)))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* (sin phi1) (sin phi2))))
#s(approx (sin phi1) #s(hole binary64 (sin phi1)))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (* (cos phi1) (cos phi2))))
#s(approx (cos phi1) #s(hole binary64 (cos phi1)))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (* (cos phi1) (cos (- lambda1 lambda2)))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* phi2 (sin phi1)) (* (cos phi1) (cos (- lambda1 lambda2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* phi2 (+ (sin phi1) (* -1/2 (* phi2 (* (cos phi1) (cos (- lambda1 lambda2))))))) (* (cos phi1) (cos (- lambda1 lambda2))))))
#s(approx (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) #s(hole binary64 (+ (* phi2 (+ (sin phi1) (* phi2 (+ (* -1/2 (* (cos phi1) (cos (- lambda1 lambda2)))) (* -1/6 (* phi2 (sin phi1))))))) (* (cos phi1) (cos (- lambda1 lambda2))))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi2 (sin phi1))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi2 (+ (sin phi1) (* -1/6 (* (pow phi2 2) (sin phi1)))))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi2 (+ (sin phi1) (* (pow phi2 2) (+ (* -1/6 (sin phi1)) (* 1/120 (* (pow phi2 2) (sin phi1)))))))))
#s(approx (* (sin phi1) (sin phi2)) #s(hole binary64 (* phi2 (+ (sin phi1) (* (pow phi2 2) (+ (* -1/6 (sin phi1)) (* (pow phi2 2) (+ (* -1/5040 (* (pow phi2 2) (sin phi1))) (* 1/120 (sin phi1))))))))))
#s(approx (sin phi2) #s(hole binary64 phi2))
#s(approx (sin phi2) #s(hole binary64 (* phi2 (+ 1 (* -1/6 (pow phi2 2))))))
#s(approx (sin phi2) #s(hole binary64 (* phi2 (+ 1 (* (pow phi2 2) (- (* 1/120 (pow phi2 2)) 1/6))))))
#s(approx (sin phi2) #s(hole binary64 (* phi2 (+ 1 (* (pow phi2 2) (- (* (pow phi2 2) (+ 1/120 (* -1/5040 (pow phi2 2)))) 1/6))))))
#s(approx phi2 #s(hole binary64 phi2))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (* (cos phi1) (cos (- lambda1 lambda2)))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* -1/2 (* (pow phi2 2) (* (cos phi1) (cos (- lambda1 lambda2))))) (* (cos phi1) (cos (- lambda1 lambda2))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* (cos phi1) (cos (- lambda1 lambda2))) (* (pow phi2 2) (+ (* -1/2 (* (cos phi1) (cos (- lambda1 lambda2)))) (* 1/24 (* (pow phi2 2) (* (cos phi1) (cos (- lambda1 lambda2))))))))))
#s(approx (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) #s(hole binary64 (+ (* (cos phi1) (cos (- lambda1 lambda2))) (* (pow phi2 2) (+ (* -1/2 (* (cos phi1) (cos (- lambda1 lambda2)))) (* (pow phi2 2) (+ (* -1/720 (* (pow phi2 2) (* (cos phi1) (cos (- lambda1 lambda2))))) (* 1/24 (* (cos phi1) (cos (- lambda1 lambda2)))))))))))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (cos phi1)))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (+ (cos phi1) (* -1/2 (* (pow phi2 2) (cos phi1))))))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (+ (cos phi1) (* (pow phi2 2) (+ (* -1/2 (cos phi1)) (* 1/24 (* (pow phi2 2) (cos phi1))))))))
#s(approx (* (cos phi1) (cos phi2)) #s(hole binary64 (+ (cos phi1) (* (pow phi2 2) (+ (* -1/2 (cos phi1)) (* (pow phi2 2) (+ (* -1/720 (* (pow phi2 2) (cos phi1))) (* 1/24 (cos phi1)))))))))
#s(approx (cos phi2) #s(hole binary64 1))
#s(approx (cos phi2) #s(hole binary64 (+ 1 (* -1/2 (pow phi2 2)))))
#s(approx (cos phi2) #s(hole binary64 (+ 1 (* (pow phi2 2) (- (* 1/24 (pow phi2 2)) 1/2)))))
#s(approx (cos phi2) #s(hole binary64 (+ 1 (* (pow phi2 2) (- (* (pow phi2 2) (+ 1/24 (* -1/720 (pow phi2 2)))) 1/2)))))
#s(approx (sin phi2) #s(hole binary64 (sin phi2)))
#s(approx (cos phi2) #s(hole binary64 (cos phi2)))

Calls

15 calls:

Time	Variable		Point	Expression
5.0ms	phi2	@	-inf	((* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2)) (sin phi1) phi1 (sin phi2) phi2 (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) (* (cos phi1) (cos phi2)) (cos phi1) (cos phi2) (cos (- lambda1 lambda2)) (- lambda1 lambda2) lambda1 lambda2 R)
4.0ms	phi2	@	0	((* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2)) (sin phi1) phi1 (sin phi2) phi2 (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) (* (cos phi1) (cos phi2)) (cos phi1) (cos phi2) (cos (- lambda1 lambda2)) (- lambda1 lambda2) lambda1 lambda2 R)
4.0ms	lambda1	@	inf	((* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2)) (sin phi1) phi1 (sin phi2) phi2 (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) (* (cos phi1) (cos phi2)) (cos phi1) (cos phi2) (cos (- lambda1 lambda2)) (- lambda1 lambda2) lambda1 lambda2 R)
3.0ms	phi1	@	-inf	((* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2)) (sin phi1) phi1 (sin phi2) phi2 (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) (* (cos phi1) (cos phi2)) (cos phi1) (cos phi2) (cos (- lambda1 lambda2)) (- lambda1 lambda2) lambda1 lambda2 R)
3.0ms	phi1	@	inf	((* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))) (* (sin phi1) (sin phi2)) (sin phi1) phi1 (sin phi2) phi2 (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))) (* (cos phi1) (cos phi2)) (cos phi1) (cos phi2) (cos (- lambda1 lambda2)) (- lambda1 lambda2) lambda1 lambda2 R)

rewrite10.0ms (0.2%)

Memory: 13.5MiB live, 13.5MiB allocated; 0ms collecting garbage

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

start0.0ms (0%)

analyze807.0ms (16.2%)

sample3.7s (75.3%)

explain334.0ms (6.7%)

preprocess42.0ms (0.8%)

series39.0ms (0.8%)

rewrite10.0ms (0.2%)

end0.0ms (0%)

Profiling