Details

Time bar (total: 1.8m)

sample959.0ms

Algorithm
intervals
Results
425.0ms139×body1280valid
112.0ms75×body640valid
28.0ms28×body320valid
7.0ms11×body160valid
1.0ms3×body80valid

simplify482.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
482.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize72.0ms

Local error

Found 4 expressions with local error:

3.4b
(cos (- lambda1 lambda2))
1.0b
(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
(* (sin phi1) (sin phi2))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
8×pow1 add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 76
Calls
4 calls:
Slowest
20.0ms
(* (sin phi1) (sin phi2))
11.0ms
(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)))))

series212.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
74.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
61.0ms
(* (sin phi1) (sin phi2))
58.0ms
(cos (- lambda1 lambda2))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify5.0s

Counts
101 → 88
Calls
101 calls:
Slowest
517.0ms
(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (* (* R R) R))
361.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
316.0ms
(* (* (* (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))))) R)) (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R))
208.0ms
(* (* (* (sin phi1) (sin phi2)) (* (sin phi1) (sin phi2))) (* (sin phi1) (sin phi2)))
163.0ms
(exp (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R))

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize111.0ms

Local error

Found 4 expressions with local error:

1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
9×associate-*r* associate-*l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 76
Calls
4 calls:
Slowest
17.0ms
(* (sin lambda1) (sin lambda2))
11.0ms
(* (sin phi1) (sin phi2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series257.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
83.0ms
(* (sin lambda1) (sin lambda2))
55.0ms
(* (sin phi1) (sin phi2))
29.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify15.0s

Counts
89 → 88
Calls
89 calls:
Slowest
462.0ms
(log1p (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
422.0ms
(sqrt (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R))
421.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))
413.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) (sqrt R))
407.0ms
(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize72.0ms

Local error

Found 4 expressions with local error:

1.0b
(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))
0.7b
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))
0.4b
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
0.3b
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 70
Calls
4 calls:
Slowest
9.0ms
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
3.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))
2.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

series98.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
44.0ms
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
28.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
16.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))
10.0ms
(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

simplify26.7s

Counts
86 → 82
Calls
86 calls:
Slowest
645.0ms
(* (* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))) (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))))
429.0ms
(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) (sqrt R))
421.0ms
(real->posit16 (* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R))
399.0ms
(log (sqrt (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))))
396.0ms
(log1p (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize100.0ms

Local error

Found 4 expressions with local error:

1.0b
(acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))
0.7b
(log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))
0.4b
(exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))
0.3b
(* (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))) R)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 70
Calls
4 calls:
Slowest
14.0ms
(* (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))) R)
5.0ms
(log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))
4.0ms
(exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))
1.0ms
(acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))

series153.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(* (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))) R)
48.0ms
(exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))
14.0ms
(log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))
10.0ms
(acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))

simplify24.8s

Counts
86 → 82
Calls
86 calls:
Slowest
687.0ms
(sqrt (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))))
417.0ms
(* (sqrt (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))) (sqrt R))
396.0ms
(* (log (exp (sqrt (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))) R)
393.0ms
(* (* (* (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2)))))) (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))) (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))) (* (* R R) R))
374.0ms
(+ (log (log (exp (acos (fma (* (cos phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) (cos phi2) (* (sin phi1) (sin phi2))))))) (log R))

prune2.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.6b

regimes1.7s

Accuracy

0% (0.5b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch10.0ms

end0.0ms

sample24.3s

Algorithm
intervals
Results
16.7s4782×body1280valid
4.8s2151×body640valid
1.9s660×body320valid
251.0ms270×body160valid
100.0ms135×body80valid
47.0ms9×body2560valid