Details

Time bar (total: 54.1s)

sample697.0ms

Algorithm
intervals
Results
440.0ms148×body1280valid
153.0ms72×body640valid
26.0ms22×body320valid
10.0ms2×body2560valid
6.0ms10×body160valid
1.0ms2×body80valid

simplify97.0ms

Calls
1 calls:
Slowest
96.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune47.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize63.0ms

Local error

Found 4 expressions with local error:

2.4b
(cos (- lambda1 lambda2))
0.8b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.2b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×cos-sum
1×acos-asin cos-diff sub-neg *-commutative fma-udef
Calls
4 calls:
Slowest
7.0ms
(cos (- lambda1 lambda2))
3.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
1.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

series331.0ms

Calls
4 calls:
Slowest
221.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
46.0ms
(cos (- lambda1 lambda2))
45.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
18.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify1.0s

Calls
18 calls:
Slowest
145.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
121.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
86.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2)))))
83.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2)))))
78.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2))))

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.3b
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.2b
(* (sin phi2) (sin phi1))
0.2b
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*r* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×*-commutative
1×acos-asin pow-prod-down prod-exp cbrt-unprod fma-udef sin-mult
Calls
4 calls:
Slowest
5.0ms
(* (sin phi2) (sin phi1))
1.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

series532.0ms

Calls
4 calls:
Slowest
412.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
66.0ms
(* (sin phi2) (sin phi1))
33.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
20.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify4.3s

Calls
24 calls:
Slowest
669.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
426.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
348.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
344.0ms
(+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))
335.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

prune1.7s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.3b
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
0.2b
(* (sin phi2) (sin phi1))
0.2b
(fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 add-cbrt-cube associate-*r* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×*-commutative
1×acos-asin pow-prod-down prod-exp cbrt-unprod fma-udef sin-mult
Calls
4 calls:
Slowest
13.0ms
(* (sin phi2) (sin phi1))
3.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
2.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.0ms
(fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))

series578.0ms

Calls
4 calls:
Slowest
441.0ms
(fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))
67.0ms
(* (sin phi2) (sin phi1))
51.0ms
(* R (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
19.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

simplify3.7s

Calls
24 calls:
Slowest
330.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
320.0ms
(* (acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2)))) R)
311.0ms
(* (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))) R)
303.0ms
(* (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))) R)
302.0ms
(+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))) (* (sin phi1) (sin phi2))))

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
0.5b
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
0.4b
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
0.3b
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×log-pow
7×associate-*r*
6×pow1
5×add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×distribute-rgt-in acos-asin distribute-lft-in
2×exp-diff
1×log-div rem-log-exp *-commutative rem-exp-log
Calls
4 calls:
Slowest
4.0ms
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
4.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
3.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))
1.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))

series108.0ms

Calls
4 calls:
Slowest
45.0ms
(* R (log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
32.0ms
(exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
16.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))
15.0ms
(log (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))

simplify9.7s

Calls
38 calls:
Slowest
396.0ms
(cbrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))
364.0ms
(acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
362.0ms
(exp (* (cbrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))) (cbrt (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1)))))))
357.0ms
(* (log (sqrt (exp (acos (fma (* (cos phi2) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (cos phi1) (* (sin phi2) (sin phi1))))))) R)
353.0ms
(acos (fma (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)) (cos phi1) (* (sin phi1) (sin phi2))))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.5b

regimes1.8s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.2b and baseline of 3.7b

bsearch7.0ms

end0.0ms

sample24.5s

Algorithm
intervals
Results
17.6s4777×body1280valid
5.2s2080×body640valid
1.1s707×body320valid
213.0ms280×body160valid
58.0ms147×body80valid
56.0ms10×body2560valid