Details

Time bar (total: 1.0m)

sample822.0ms

Algorithm
intervals
Results
484.0ms153×body1280valid
159.0ms67×body640valid
77.0ms25×body320valid
5.0ms7×body160valid
4.0ms1×body2560valid
1.0ms3×body80valid

simplify118.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
118.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize66.0ms

Local error

Found 4 expressions with local error:

4.3b
(cos (- lambda1 lambda2))
1.0b
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.3b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
11×cos-sum
9×prod-diff
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
1×acos-asin cos-diff sub-neg pow-prod-down prod-exp *-commutative cbrt-unprod fma-udef unswap-sqr
Counts
4 → 65
Calls
4 calls:
Slowest
19.0ms
(cos (- lambda1 lambda2))
6.0ms
(* 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))))
0.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
243.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
40.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
35.0ms
(cos (- lambda1 lambda2))
23.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.3s

Counts
34 → 77
Calls
34 calls:
Slowest
485.0ms
(* (* (* R R) R) (* (* (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))) (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))) (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
177.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
130.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
97.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
83.0ms
(sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.0b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
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 fma-udef sin-mult
Counts
4 → 65
Calls
4 calls:
Slowest
12.0ms
(* (sin lambda1) (sin lambda2))
12.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
2.0ms
(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)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
380.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
59.0ms
(* (sin lambda1) (sin lambda2))
38.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
11.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify6.6s

Counts
33 → 77
Calls
33 calls:
Slowest
784.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
420.0ms
(cbrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
419.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
412.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
396.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*l* add-cube-cbrt
7×associate-*r*
5×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×*-commutative
2×unswap-sqr
1×acos-asin associate-*r/ cos-mult sin-mult
Counts
4 → 76
Calls
4 calls:
Slowest
31.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
12.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
282.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
57.0ms
(* (sin lambda1) (sin lambda2))
41.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
15.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))

simplify6.8s

Counts
42 → 88
Calls
42 calls:
Slowest
461.0ms
(* (sqrt R) (sqrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
383.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
380.0ms
(sqrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
374.0ms
(+ (log R) (log (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
367.0ms
(* (sqrt R) (sqrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))

prune2.3s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.9b

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b
(log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))
1.0b
(acos (fma (sin phi1) (sin phi2) (log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
0.2b
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
0.2b
(* R (acos (fma (sin phi1) (sin phi2) (log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
11×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×associate-*l*
5×add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
3×log-prod log-pow
2×*-commutative
1×acos-asin exp-prod exp-to-pow rem-log-exp associate-*r/ cos-mult unswap-sqr
Counts
4 → 71
Calls
4 calls:
Slowest
30.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
7.0ms
(log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))
6.0ms
(* R (acos (fma (sin phi1) (sin phi2) (log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))

series596.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
276.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
245.0ms
(log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))
57.0ms
(* R (acos (fma (sin phi1) (sin phi2) (log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))))
19.0ms
(acos (fma (sin phi1) (sin phi2) (log (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))

simplify7.2s

Counts
37 → 83
Calls
37 calls:
Slowest
392.0ms
(log (* (cbrt (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))) (cbrt (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
363.0ms
(log (sqrt (exp (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
351.0ms
(* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))
351.0ms
(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
345.0ms
(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))

prune2.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 3.9b

regimes1.1s

Accuracy

0% (0.3b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch4.0ms

end0.0ms

sample25.3s

Algorithm
intervals
Results
17.7s4811×body1280valid
5.1s2082×body640valid
1.3s693×body320valid
457.0ms140×body80valid
213.0ms266×body160valid
45.0ms9×body2560valid