Details

Time bar (total: 12.5s)

sample268.0ms

Algorithm
intervals
Results
196.0ms163×body1280valid
44.0ms67×body640valid
7.0ms16×body320valid
2.0ms6×body160valid
1.0ms4×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b
(cos (- lambda1 lambda2))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
10.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

series185.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
46.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
11.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
24.0ms
(cos (- lambda1 lambda2))

simplify107.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0264773
11022656
24705656
35002656

prune335.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r* cos-mult
7×associate-*l*
5×pow-prod-down prod-exp cbrt-unprod sin-mult
4×frac-times associate-*r/ add-log-exp
3×*-commutative
2×distribute-rgt-in sub-neg flip3-- distribute-lft-in frac-sub flip-- sub-div unswap-sqr
1×acos-asin associate-*l/
Counts
4 → 76
Calls
4 calls:
4.0ms
(* (sin phi1) (sin phi2))
25.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (sin phi1) (sin phi2))
210.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
75.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04881460
120381228
250021221

prune503.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.3b
(pow (* (sin phi1) (sin phi2)) 3)
0.8b
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
26.2b
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 add-exp-log add-cbrt-cube
8×cbrt-prod add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×pow-unpow associate-*r* associate-*l*
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod sin-mult rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 67
Calls
4 calls:
3.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
3.0ms
(pow (* (sin phi1) (sin phi2)) 3)
2.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
2.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series206.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
68.0ms
(pow (* (sin phi1) (sin phi2)) 3)
18.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
46.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify186.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02971078
11032937
24944925
35001925

prune485.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.3b
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))) R)
0.5b
(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.6b
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
11×pow1 add-exp-log *-un-lft-identity add-cbrt-cube
9×cos-mult
7×add-cube-cbrt associate-*l*
6×associate-*r* add-log-exp
4×frac-times flip3-- associate-*r/ pow-prod-down prod-exp flip-- cbrt-unprod sin-mult difference-of-squares
3×sub-neg associate-*l/
2×distribute-rgt-in asin-acos distribute-lft-in times-frac *-commutative frac-sub distribute-lft-out-- sub-div
1×diff-log associate--r- unswap-sqr
Counts
4 → 78
Calls
4 calls:
27.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
35.0ms
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))) R)
1.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
11.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
213.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
178.0ms
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))) R)
18.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
58.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

simplify65.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05132051
120641833
250021825

prune478.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 1.9b

regimes545.0ms

Accuracy

0% (0.6b remaining)

Error of 3.9b against oracle of 3.3b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03522
13522

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.8s4817×body1280valid
1.4s2045×body640valid
315.0ms711×body320valid
80.0ms282×body160valid
21.0ms7×body2560valid
21.0ms142×body80valid