Details

Time bar (total: 20.0s)

sample238.0ms

Algorithm
intervals
Results
149.0ms114×body1280valid
48.0ms76×body640valid
13.0ms31×body320valid
4.0ms25×body80valid
3.0ms10×body160valid

simplify2.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0b
(sin (- lambda1 lambda2))
3.1b
(cos (- lambda1 lambda2))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
3×cos-diff
2×sub-neg cos-sum associate-+r+ sin-sum
1×+-commutative distribute-rgt-in distribute-lft-in flip3-+ sum-log sin-diff flip-+
Counts
4 → 40
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
10.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
14.0ms
(sin (- lambda1 lambda2))
42.0ms
(cos (- lambda1 lambda2))

series181.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
123.0ms
(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
24.0ms
(sin (- lambda1 lambda2))
21.0ms
(cos (- lambda1 lambda2))

simplify114.0ms

Counts
52 → 52

prune266.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.7b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
3.0b
(sin (- lambda1 lambda2))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
4×associate-+r+
3×sub-neg associate-*r* associate-*l*
2×distribute-rgt-in distribute-lft-in sin-sum
1×+-commutative flip3-+ pow-prod-down prod-exp sin-neg sum-log sin-diff *-commutative distribute-rgt-neg-out cbrt-unprod flip-+ sin-mult unswap-sqr
Counts
4 → 52
Calls
4 calls:
0.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
16.0ms
(* (sin lambda1) (sin (- lambda2)))
10.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
17.0ms
(sin (- lambda1 lambda2))

series367.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
58.0ms
(* (sin lambda1) (sin (- lambda2)))
265.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
24.0ms
(sin (- lambda1 lambda2))

simplify79.0ms

Counts
64 → 64

prune372.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.2b
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.5b
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×associate-+r+
3×distribute-rgt-in distribute-lft-in
2×sub-neg flip3-+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sin-neg sum-log distribute-rgt-neg-out sin-mult
Counts
4 → 64
Calls
4 calls:
47.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
0.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
16.0ms
(* (sin lambda1) (sin (- lambda2)))
10.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series506.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))))
21.0ms
(atan2 (* (cos phi2) (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
57.0ms
(* (sin lambda1) (sin (- lambda2)))
263.0ms
(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify47.0ms

Counts
76 → 76

prune446.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
0.4b
(pow (cos phi1) 3)
0.6b
(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
1.1b
(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite493.0ms

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity
22×cos-mult
18×add-sqr-sqrt add-cube-cbrt associate-*r/
16×associate-/r/
15×times-frac
14×frac-add
10×add-exp-log flip3-- add-cbrt-cube flip--
8×pow1 frac-times sin-mult
6×pow-unpow add-log-exp
5×associate-/l*
4×cube-div unpow-prod-down cube-prod associate-*l/ associate--l+ sum-cubes frac-sub distribute-lft-out sub-div
3×sub-neg pow-pow pow-exp associate-/r* rem-cube-cbrt
2×distribute-rgt-in cube-mult pow-to-exp distribute-lft-in flip3-+ unpow3 flip-+ associate-/l/ sqr-pow
1×cbrt-undiv frac-2neg diff-log div-exp pow-prod-down prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 118
Calls
4 calls:
369.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
4.0ms
(pow (cos phi1) 3)
40.0ms
(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
76.0ms
(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

series5.4s

Counts
4 → 12
Calls
4 calls:
4.9s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
34.0ms
(pow (cos phi1) 3)
239.0ms
(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
249.0ms
(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify59.0ms

Counts
130 → 130

prune959.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes554.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
5.9s3601×body1280valid
2.1s2329×body640valid
796.0ms931×body320valid
130.0ms472×body160valid
127.0ms667×body80valid