Average Error: 16.8 → 3.8
Time: 49.0s
Precision: 64
Internal Precision: 128
\[\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)\right) \cdot R\]
↓
\[R \cdot \log \left(e^{\cos^{-1} \left(\sin \phi_2 \cdot \sin \phi_1 + \left(\sqrt[3]{{\left(\sin \lambda_2 \cdot \sin \lambda_1\right)}^{3}} \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\left(\cos \lambda_1 \cdot \cos \lambda_2\right) \cdot \cos \phi_2\right) \cdot \cos \phi_1\right)\right)}\right)\]

Error

Bits error versus R

Bits error versus lambda1

Bits error versus lambda2

Bits error versus phi1

Bits error versus phi2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.8

    \[\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \cos \left(\lambda_1 - \lambda_2\right)\right) \cdot R\]
  2. Using strategy rm

  3. Applied cos-diff3.8

    \[\leadsto \cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \color{blue}{\left(\cos \lambda_1 \cdot \cos \lambda_2 + \sin \lambda_1 \cdot \sin \lambda_2\right)}\right) \cdot R\]

  4. Applied distribute-lft-in3.8

    \[\leadsto \cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \color{blue}{\left(\left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2\right) + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right)}\right) \cdot R\]
  5. Using strategy rm

  6. Applied associate-*l*3.8

    \[\leadsto \cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\color{blue}{\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2\right)\right)} + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right)\right) \cdot R\]
  7. Using strategy rm

  8. Applied add-log-exp3.8

    \[\leadsto \color{blue}{\log \left(e^{\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2\right)\right) + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\sin \lambda_1 \cdot \sin \lambda_2\right)\right)\right)}\right)} \cdot R\]
  9. Using strategy rm

  10. Applied add-cbrt-cube3.8

    \[\leadsto \log \left(e^{\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2\right)\right) + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\sin \lambda_1 \cdot \color{blue}{\sqrt[3]{\left(\sin \lambda_2 \cdot \sin \lambda_2\right) \cdot \sin \lambda_2}}\right)\right)\right)}\right) \cdot R\]

  11. Applied add-cbrt-cube3.9

    \[\leadsto \log \left(e^{\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2\right)\right) + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \left(\color{blue}{\sqrt[3]{\left(\sin \lambda_1 \cdot \sin \lambda_1\right) \cdot \sin \lambda_1}} \cdot \sqrt[3]{\left(\sin \lambda_2 \cdot \sin \lambda_2\right) \cdot \sin \lambda_2}\right)\right)\right)}\right) \cdot R\]

  12. Applied cbrt-unprod3.8

    \[\leadsto \log \left(e^{\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2\right)\right) + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \color{blue}{\sqrt[3]{\left(\left(\sin \lambda_1 \cdot \sin \lambda_1\right) \cdot \sin \lambda_1\right) \cdot \left(\left(\sin \lambda_2 \cdot \sin \lambda_2\right) \cdot \sin \lambda_2\right)}}\right)\right)}\right) \cdot R\]

  13. Simplified3.8

    \[\leadsto \log \left(e^{\cos^{-1} \left(\sin \phi_1 \cdot \sin \phi_2 + \left(\cos \phi_1 \cdot \left(\cos \phi_2 \cdot \left(\cos \lambda_1 \cdot \cos \lambda_2\right)\right) + \left(\cos \phi_1 \cdot \cos \phi_2\right) \cdot \sqrt[3]{\color{blue}{{\left(\sin \lambda_2 \cdot \sin \lambda_1\right)}^{3}}}\right)\right)}\right) \cdot R\]

  14. Final simplification3.8

    \[\leadsto R \cdot \log \left(e^{\cos^{-1} \left(\sin \phi_2 \cdot \sin \phi_1 + \left(\sqrt[3]{{\left(\sin \lambda_2 \cdot \sin \lambda_1\right)}^{3}} \cdot \left(\cos \phi_1 \cdot \cos \phi_2\right) + \left(\left(\cos \lambda_1 \cdot \cos \lambda_2\right) \cdot \cos \phi_2\right) \cdot \cos \phi_1\right)\right)}\right)\]

Reproduce

herbie shell --seed 2019010 
(FPCore (R lambda1 lambda2 phi1 phi2)
  :name "Spherical law of cosines"
  (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R))

Details

Time bar (total: 44.9s)Debug log

sample845.0ms

Algorithm
intervals

simplify47.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
47.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize73.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (- lambda1 lambda2))
0.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log
9×add-cbrt-cube
9×pow1
6×add-cube-cbrt
6×*-un-lft-identity
6×add-sqr-sqrt
4×add-log-exp
4×associate-*l*
3×cbrt-unprod
3×prod-exp
3×pow-prod-down
3×associate-*r*
3×cos-diff
2×*-commutative
2×cos-sum
1×cos-mult
1×associate-*l/
1×distribute-lft-in
1×sub-neg
1×acos-asin
1×distribute-rgt-in
Counts
4 → 50
Calls
4 calls:
Slowest
14.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0ms
(cos (- lambda1 lambda2))
5.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series236.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
79.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
22.0ms
(cos (- lambda1 lambda2))
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify995.0ms

Counts
30 → 62
Calls
30 calls:
Slowest
252.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
196.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
92.0ms
(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
53.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
32.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
18×add-cbrt-cube
18×pow1
9×cbrt-unprod
9×prod-exp
9×pow-prod-down
7×add-cube-cbrt
7×associate-*l*
7×*-un-lft-identity
7×add-sqr-sqrt
4×add-log-exp
4×cos-mult
4×associate-*r*
3×*-commutative
1×sin-mult
1×associate-*r/
1×associate-*l/
1×frac-times
1×acos-asin
Counts
4 → 62
Calls
4 calls:
Slowest
18.0ms
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
3.0ms
(* (sin lambda1) (sin lambda2))
2.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
76.0ms
(* (sin lambda1) (sin lambda2))
62.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
26.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify2.7s

Counts
40 → 74
Calls
40 calls:
Slowest
694.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (cos lambda1) (cos lambda2))))
155.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
135.0ms
(* (acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))) R)
128.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))
128.0ms
(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))

prune1.9s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b
(* (sin lambda1) (sin lambda2))
0.2b
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
18×add-cbrt-cube
18×pow1
9×cbrt-unprod
9×prod-exp
9×pow-prod-down
7×add-cube-cbrt
7×associate-*l*
7×*-un-lft-identity
7×add-sqr-sqrt
4×add-log-exp
4×associate-*r*
3×sin-mult
3×*-commutative
2×cos-mult
1×associate-*r/
1×associate-*l/
1×frac-times
1×acos-asin
Counts
4 → 62
Calls
4 calls:
Slowest
19.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
3.0ms
(* (sin lambda1) (sin lambda2))
2.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
86.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
76.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Counts
40 → 74
Calls
40 calls:
Slowest
715.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin lambda1) (sin lambda2))))
184.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))
159.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
150.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
130.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
0.3b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.3b
(* (sin lambda1) (sin lambda2))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*l*
9×add-cube-cbrt
9×*-un-lft-identity
9×add-sqr-sqrt
7×pow1
6×add-exp-log
6×add-cbrt-cube
6×exp-prod
5×add-log-exp
4×log-pow
3×associate-*r*
2×*-commutative
2×acos-asin
1×rem-exp-log
1×sin-mult
1×cbrt-unprod
1×prod-exp
1×pow-prod-down
1×exp-diff
Counts
4 → 53
Calls
4 calls:
Slowest
10.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
6.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series264.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))) R)
82.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
59.0ms
(* (sin lambda1) (sin lambda2))
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify2.3s

Counts
31 → 65
Calls
31 calls:
Slowest
193.0ms
(* (cbrt (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))) (cbrt (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))))
191.0ms
(exp (* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))))
169.0ms
(cbrt (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))))
150.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))
149.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

prune1.8s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.6b

regimes2.2s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch7.0ms

end0.0ms

sample24.7s

Algorithm
intervals