Details

Time bar (total: 12.5s)

sample251.0ms

Algorithm
intervals
Results
181.0ms158×body1280valid
43.0ms66×body640valid
8.0ms20×body320valid
2.0ms7×body160valid
1.0ms5×body80valid

simplify6.0ms

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: 15.9b

localize29.0ms

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)
0.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b
(cos (- lambda1 lambda2))

rewrite16.0ms

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:
6.0ms
(* (* (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)))))
4.0ms
(cos (- lambda1 lambda2))

series190.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
46.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms
(cos (- lambda1 lambda2))

simplify103.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0264773
11022656
24705656
35002656

prune311.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.9b

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)
0.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite25.0ms

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:
5.0ms
(* (sin phi1) (sin phi2))
13.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
4.0ms
(* (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)))))))

series339.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin phi1) (sin phi2))
207.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
71.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify63.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04881460
120381228
250021221

prune467.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.8b

localize39.0ms

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)
0.4b
(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))))))))

rewrite31.0ms

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:
11.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
10.0ms
(* (- (/ 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)))))))
7.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
209.0ms
(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
168.0ms
(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))) R)
16.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
59.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05132051
120641833
250021825

prune566.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
0.6b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.6b
(- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
1.2b
(- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×*-un-lft-identity
11×add-log-exp
7×associate-*l* distribute-lft-out--
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube difference-of-squares
5×flip3-- flip--
4×diff-log associate-*l/ frac-sub
3×acos-asin sub-neg times-frac associate-*r* associate--r+ associate--r-
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 73
Calls
4 calls:
18.0ms
(* (- (/ PI 2) (- (/ PI 2) (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)))))))
16.0ms
(- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
8.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

series171.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
19.0ms
(- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
60.0ms
(- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
03272442
19732217
250022156

prune453.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.6b

regimes696.0ms

Accuracy

0% (0.6b remaining)

Error of 3.6b against oracle of 3.1b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04062
14062

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.9s4771×body1280valid
1.4s2120×body640valid
308.0ms690×body320valid
81.0ms280×body160valid
24.0ms7×body2560valid
20.0ms132×body80valid