Details

Time bar (total: 1.1m)

sample951.0ms

Algorithm
intervals
Results
584.0ms138×body1280valid
209.0ms81×body640valid
27.0ms19×body320valid
10.0ms13×body160valid
2.0ms5×body80valid

simplify68.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
67.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune62.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.9b

localize83.0ms

Local error

Found 4 expressions with local error:

2.0b
(cos (- lambda1 lambda2))
1.7b
(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)))

rewrite40.0ms

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
24.0ms
(cos (- lambda1 lambda2))
12.0ms
(* 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)))

series400.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
282.0ms
(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
56.0ms
(cos (- lambda1 lambda2))
44.0ms
(* 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))))

simplify2.4s

Counts
34 → 77
Calls
34 calls:
Slowest
508.0ms
(* (* (* 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))))))
181.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
142.0ms
(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
85.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi1) (sin phi2)))))
84.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.5b

localize115.0ms

Local error

Found 4 expressions with local error:

1.7b
(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))

rewrite39.0ms

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
24.0ms
(* (sin phi2) (sin phi1))
12.0ms
(* 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)))

series909.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
779.0ms
(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
62.0ms
(* (sin phi2) (sin phi1))
47.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
21.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify6.2s

Counts
33 → 77
Calls
33 calls:
Slowest
412.0ms
(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
411.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
399.0ms
(sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
383.0ms
(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
361.0ms
(+ (log R) (log (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.3b

localize103.0ms

Local error

Found 4 expressions with local error:

1.7b
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
1.2b
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
0.4b
(exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.3b
(* R (log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in acos-asin distribute-lft-in associate-*l*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr rem-exp-log
Counts
4 → 76
Calls
4 calls:
Slowest
11.0ms
(* R (log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))))
3.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
2.0ms
(exp (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))))

series99.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
43.0ms
(exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
31.0ms
(* R (log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))))
13.0ms
(log (exp (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))))

simplify13.8s

Counts
45 → 88
Calls
45 calls:
Slowest
462.0ms
(* R (log (cbrt (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))))
422.0ms
(* (log (cbrt (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))) R)
418.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
416.0ms
(log (exp (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))))
399.0ms
(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

prune2.7s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.3b

localize61.0ms

Local error

Found 4 expressions with local error:

1.7b
(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))
0.3b
(* (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))) R)
0.2b
(* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
0.1b
(fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-cbrt-cube add-exp-log
9×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×associate-*r*
4×expm1-log1p-u associate-*l* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
2×*-commutative
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 67
Calls
4 calls:
Slowest
42.0ms
(* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
7.0ms
(* (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))) R)
1.0ms
(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))
0.0ms
(fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))

series782.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
406.0ms
(fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))
289.0ms
(* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
68.0ms
(* (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))) R)
19.0ms
(acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))

simplify7.5s

Counts
34 → 79
Calls
34 calls:
Slowest
615.0ms
(acos (fma (sin phi2) (sin phi1) (* (cos phi1) (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (cos phi2)))))
356.0ms
(* (sqrt (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))))) (sqrt R))
351.0ms
(sqrt (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))))
344.0ms
(* (acos (fma (sin phi2) (sin phi1) (* (* (cos phi2) (cos phi1)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))) R)
327.0ms
(* (* (* (* (cos phi2) (cos phi1)) (* (cos phi2) (cos phi1))) (* (cos phi2) (cos phi1))) (* (* (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))))

prune2.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.3b

regimes1.4s

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch9.0ms

end0.0ms

sample24.7s

Algorithm
intervals
Results
17.3s4761×body1280valid
5.7s2165×body640valid
982.0ms658×body320valid
218.0ms284×body160valid
50.0ms126×body80valid
43.0ms7×body2560valid