Details

Time bar (total: 50.8s)

sample1.4s

Algorithm
intervals
Results
673.0ms74×body640valid
608.0ms146×body1280valid
31.0ms28×body320valid
6.0ms8×body160valid

simplify88.0ms

Calls
1 calls:
Slowest
87.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize81.0ms

Local error

Found 4 expressions with local error:

5.1b
(cos (- lambda1 lambda2))
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-cbrt-cube add-exp-log
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×cos-diff associate-*r* pow-prod-down prod-exp cbrt-unprod
2×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult
Calls
4 calls:
Slowest
42.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms
(cos (- lambda1 lambda2))
6.0ms
(* (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)))))

series242.0ms

Calls
4 calls:
Slowest
118.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
66.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
38.0ms
(cos (- lambda1 lambda2))
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify2.2s

Calls
30 calls:
Slowest
471.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
402.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (cos (- lambda1 lambda2)) (cos (- lambda1 lambda2))) (cos (- lambda1 lambda2))))
274.0ms
(- 1 (+ (* 1/2 (pow phi2 2)) (* 1/2 (pow phi1 2))))
164.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
91.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity associate-*l* add-cube-cbrt
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×pow-prod-down prod-exp cbrt-unprod sin-mult
1×acos-asin
Calls
4 calls:
Slowest
9.0ms
(* (sin phi1) (sin phi2))
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series210.0ms

Calls
4 calls:
Slowest
69.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
62.0ms
(* (sin phi1) (sin phi2))
54.0ms
(* (sin lambda1) (sin lambda2))
25.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.8s

Calls
32 calls:
Slowest
403.0ms
(sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
342.0ms
(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
330.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
313.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
285.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2)))))

prune2.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))
0.2b
(* (sin lambda2) (sin lambda1))
0.2b
(* (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))) R)
0.2b
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×associate-*l*
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
1×acos-asin associate-*r/ cos-mult sin-mult
Calls
4 calls:
Slowest
20.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))
8.0ms
(* (sin lambda2) (sin lambda1))
6.0ms
(* (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))) R)
1.0ms
(acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))

series332.0ms

Calls
4 calls:
Slowest
192.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))
72.0ms
(* (sin lambda2) (sin lambda1))
49.0ms
(* (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))) R)
20.0ms
(acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))

simplify4.0s

Calls
32 calls:
Slowest
351.0ms
(* (cbrt (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))) (cbrt (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))
341.0ms
(* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))
310.0ms
(sqrt (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
309.0ms
(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (cos phi2))))) R)
297.0ms
(* (acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))) R)

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))
0.6b
(log (exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))
0.3b
(exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
0.2b
(* (sin lambda2) (sin lambda1))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×exp-prod add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u log-pow insert-posit16 log1p-expm1-u
3×acos-asin log-prod associate-*r* associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult rem-exp-log
Calls
4 calls:
Slowest
9.0ms
(* (sin lambda2) (sin lambda1))
5.0ms
(log (exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))
4.0ms
(exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
1.0ms
(acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))

series146.0ms

Calls
4 calls:
Slowest
57.0ms
(* (sin lambda2) (sin lambda1))
45.0ms
(exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
24.0ms
(log (exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))
20.0ms
(acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))

simplify5.6s

Calls
34 calls:
Slowest
379.0ms
(log (* (cbrt (exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))) (cbrt (exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))))))
373.0ms
(log (sqrt (exp (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))))
354.0ms
(sqrt (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))
346.0ms
(exp (* (cbrt (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1)))))) (cbrt (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))))
344.0ms
(cbrt (acos (fma (sin phi2) (sin phi1) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (cos phi2) (cos phi1))))))

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.9b

regimes1.6s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch7.0ms

end0.0ms

sample24.3s

Algorithm
intervals
Results
17.6s4789×body1280valid
5.0s2131×body640valid
983.0ms671×body320valid
304.0ms278×body160valid
70.0ms10×body2560valid
46.0ms127×body80valid