Details

Time bar (total: 57.2s)

sample1.1s

Algorithm
intervals
Results
785.0ms145×body1280valid
127.0ms73×body640valid
28.0ms23×body320valid
6.0ms10×body160valid
2.0ms5×body80valid

simplify115.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
115.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune46.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize65.0ms

Local error

Found 4 expressions with local error:

4.3b
(cos (- lambda1 lambda2))
1.1b
(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)))))
0.3b
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

rewrite29.0ms

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
20.0ms
(cos (- lambda1 lambda2))
5.0ms
(* 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)))

series309.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
38.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
38.0ms
(cos (- lambda1 lambda2))
10.0ms
(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.2s

Counts
34 → 77
Calls
34 calls:
Slowest
389.0ms
(* (* (* 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))))))
173.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
146.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
91.0ms
(+ (log R) (log (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
87.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.8b

localize86.0ms

Local error

Found 4 expressions with local error:

1.1b
(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
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
0.2b
(* (sin phi2) (sin phi1))

rewrite32.0ms

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
22.0ms
(* (sin phi2) (sin phi1))
8.0ms
(* 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)))

series539.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
389.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
79.0ms
(* (sin phi2) (sin phi1))
52.0ms
(* 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))))

simplify5.6s

Counts
33 → 77
Calls
33 calls:
Slowest
386.0ms
(sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
354.0ms
(+ (log R) (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
343.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
343.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
325.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))

prune1.9s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.7b

localize73.0ms

Local error

Found 4 expressions with local error:

1.1b
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))
0.3b
(* 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))
0.2b
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))

rewrite54.0ms

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
23.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
18.0ms
(* (sin lambda1) (sin lambda2))
12.0ms
(* 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)))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
266.0ms
(* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))
61.0ms
(* (sin lambda1) (sin lambda2))
50.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1))))))
16.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))

simplify6.7s

Counts
42 → 88
Calls
42 calls:
Slowest
408.0ms
(* (sqrt R) (sqrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)))))))
383.0ms
(cbrt (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)))))))
369.0ms
(* (acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))))))) R)
366.0ms
(* (cos phi1) (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (cos phi2)))

prune2.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.6b

localize91.0ms

Local error

Found 4 expressions with local error:

2.1b
(log (exp (* (sin lambda1) (sin lambda2))))
1.1b
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1)))))
0.3b
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1))))))
0.2b
(* (sin lambda1) (sin lambda2))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 *-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×associate-*r* associate-*l*
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×log-prod log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin exp-prod exp-to-pow rem-log-exp sin-mult
Counts
4 → 71
Calls
4 calls:
Slowest
11.0ms
(* (sin lambda1) (sin lambda2))
7.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
5.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1))))))
1.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1)))))

series207.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
81.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
74.0ms
(* (sin lambda1) (sin lambda2))
33.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1))))))
19.0ms
(acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1)))))

simplify5.2s

Counts
39 → 83
Calls
39 calls:
Slowest
407.0ms
(* (* (* (sin lambda1) (sin lambda1)) (sin lambda1)) (* (* (sin lambda2) (sin lambda2)) (sin lambda2)))
356.0ms
(sqrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1))))))
351.0ms
(acos (fma (sin phi1) (sin phi2) (* (cos phi1) (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))))))
347.0ms
(* R (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1))))))
341.0ms
(cbrt (acos (fma (sin phi1) (sin phi2) (* (fma (cos lambda2) (cos lambda1) (log (exp (* (sin lambda1) (sin lambda2))))) (* (cos phi2) (cos phi1))))))

prune2.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.6b

regimes2.0s

Accuracy

0% (0.4b remaining)

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

bsearch10.0ms

end0.0ms

sample24.0s

Algorithm
intervals
Results
16.7s4788×body1280valid
4.7s2073×body640valid
1.9s702×body320valid
218.0ms288×body160valid
67.0ms11×body2560valid
59.0ms143×body80valid