Details

Time bar (total: 47.1s)

sample1.1s

Algorithm
intervals
Results
511.0ms150×body1280valid
467.0ms64×body640valid
32.0ms27×body320valid
6.0ms7×body160valid
4.0ms1×body2560valid
3.0ms7×body80valid

simplify60.0ms

Calls
1 calls:
Slowest
59.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize41.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (- lambda1 lambda2))
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b
(* (sin phi1) (sin phi2))

rewrite71.0ms

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×insert-posit16 add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Calls
4 calls:
Slowest
37.0ms
(* (sin phi1) (sin phi2))
16.0ms
(cos (- lambda1 lambda2))
11.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series175.0ms

Calls
4 calls:
Slowest
62.0ms
(* (sin phi1) (sin phi2))
49.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
44.0ms
(cos (- lambda1 lambda2))
19.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.6s

Calls
35 calls:
Slowest
537.0ms
(* (* (* (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))
269.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
95.0ms
(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
74.0ms
(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (log R))
58.0ms
(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.1b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b
(* (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
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log
9×*-un-lft-identity associate-*r* add-cube-cbrt
7×associate-*l*
6×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×insert-posit16 add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Calls
4 calls:
Slowest
64.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (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))))))

series462.0ms

Calls
4 calls:
Slowest
279.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
99.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
66.0ms
(* (sin phi1) (sin phi2))
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify7.6s

Calls
54 calls:
Slowest
565.0ms
(* (* (* (* (cos phi1) (cos phi2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
562.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (+ (* (+ (cos (+ lambda1 lambda2)) (cos (- lambda1 lambda2))) 2) (* 2 (- (cos (- lambda1 lambda2)) (cos (+ lambda1 lambda2))))))
486.0ms
(* (* (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (cos phi2)) (cos phi2))) (* (* (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
385.0ms
(* (+ (cos (+ phi1 phi2)) (cos (- phi1 phi2))) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))))
372.0ms
(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))

prune2.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.0b

localize127.0ms

Local error

Found 4 expressions with local error:

8.9b
(cbrt (* (sin phi1) (sin phi2)))
8.9b
(cbrt (* (sin phi1) (sin phi2)))
8.9b
(cbrt (* (sin phi1) (sin phi2)))
0.5b
(acos (+ (* (* (cbrt (* (sin phi1) (sin phi2))) (cbrt (* (sin phi1) (sin phi2)))) (cbrt (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
3×cbrt-prod cbrt-div pow1/3 sin-mult
1×acos-asin
Calls
4 calls:
Slowest
10.0ms
(cbrt (* (sin phi1) (sin phi2)))
10.0ms
(cbrt (* (sin phi1) (sin phi2)))
10.0ms
(cbrt (* (sin phi1) (sin phi2)))
3.0ms
(acos (+ (* (* (cbrt (* (sin phi1) (sin phi2))) (cbrt (* (sin phi1) (sin phi2)))) (cbrt (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series426.0ms

Calls
4 calls:
Slowest
152.0ms
(cbrt (* (sin phi1) (sin phi2)))
127.0ms
(cbrt (* (sin phi1) (sin phi2)))
118.0ms
(cbrt (* (sin phi1) (sin phi2)))
29.0ms
(acos (+ (* (* (cbrt (* (sin phi1) (sin phi2))) (cbrt (* (sin phi1) (sin phi2)))) (cbrt (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.1s

Calls
18 calls:
Slowest
455.0ms
(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
383.0ms
(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
379.0ms
(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
187.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))
182.0ms
(acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.0b

localize83.0ms

Local error

Found 4 expressions with local error:

8.9b
(cbrt (* (sin phi1) (sin phi2)))
8.9b
(cbrt (* (sin phi1) (sin phi2)))
0.6b
(cbrt (sin phi2))
0.6b
(cbrt (sin phi1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 add-cbrt-cube pow1/3 add-exp-log insert-posit16 add-log-exp
2×cbrt-div sin-mult
Calls
4 calls:
Slowest
5.0ms
(cbrt (* (sin phi1) (sin phi2)))
5.0ms
(cbrt (* (sin phi1) (sin phi2)))
1.0ms
(cbrt (sin phi2))
1.0ms
(cbrt (sin phi1))

series531.0ms

Calls
4 calls:
Slowest
145.0ms
(cbrt (sin phi2))
143.0ms
(cbrt (sin phi1))
125.0ms
(cbrt (* (sin phi1) (sin phi2)))
118.0ms
(cbrt (* (sin phi1) (sin phi2)))

simplify1.6s

Calls
22 calls:
Slowest
360.0ms
(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
319.0ms
(- (exp (* 1/3 (+ (log phi1) (log phi2)))) (+ (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi1 2))) (* 1/18 (* (exp (* 1/3 (+ (log phi1) (log phi2)))) (pow phi2 2)))))
288.0ms
(- (pow phi1 1/3) (+ (* 1/3240 (pow (pow phi1 13) 1/3)) (* 1/18 (pow (pow phi1 7) 1/3))))
251.0ms
(- (pow phi2 1/3) (+ (* 1/3240 (pow (pow phi2 13) 1/3)) (* 1/18 (pow (pow phi2 7) 1/3))))
63.0ms
(pow (* (sin phi1) (sin phi2)) 1/3)

prune1.6s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.0b

regimes1.0s

Accuracy

0% (0.5b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch7.0ms

end0.0ms

sample23.3s

Algorithm
intervals
Results
16.1s4779×body1280valid
5.5s2132×body640valid
1.0s681×body320valid
186.0ms249×body160valid
108.0ms149×body80valid
60.0ms10×body2560valid