Details

Time bar (total: 12.3s)

sample281.0ms

Algorithm
intervals
Results
208.0ms168×body1280valid
43.0ms56×body640valid
9.0ms19×body320valid
3.0ms11×body160valid
0.0ms2×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize24.0ms

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)
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.7b
(cos (- lambda1 lambda2))

rewrite18.0ms

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:
9.0ms
(* (* (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))

series171.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
44.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms
(cos (- lambda1 lambda2))

simplify108.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
0264773
11022656
24705656
35002656

prune298.0ms

Filtered
69 candidates to 49 candidates (71.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
20×pow1 add-exp-log add-cbrt-cube
12×add-sqr-sqrt
10×pow-prod-down prod-exp cbrt-unprod
8×add-cube-cbrt *-un-lft-identity
7×associate-*r* associate-*l*
4×add-log-exp
3×*-commutative sin-mult
2×cos-mult unswap-sqr
1×acos-asin frac-times associate-*r/ associate-*l/
Counts
4 → 70
Calls
4 calls:
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
13.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series258.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (sin lambda2))
73.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
124.0ms
(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify42.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
03111247
111961031
250021031

prune409.0ms

Filtered
82 candidates to 50 candidates (61.0%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))) R)
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 64
Calls
4 calls:
4.0ms
(* (sin phi1) (sin phi2))
4.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

series174.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin phi1) (sin phi2))
46.0ms
(* (sin lambda1) (sin lambda2))
68.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))) R)
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

simplify80.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
02711065
1844910
21937910
33101910
45001910

prune436.0ms

Filtered
76 candidates to 51 candidates (67.1%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 2.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))))) R)
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))))
0.7b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 58
Calls
4 calls:
6.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))))) R)
1.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))))
2.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

series148.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))))) R)
43.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))))
19.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))))
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))))

simplify120.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 4 (42.0ms)

IterNodesCost
01911853
14091609
29241603
312861603
435431599
550021599

prune352.0ms

Filtered
70 candidates to 48 candidates (68.6%)
Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 2.1b

regimes1.1s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03623
13623

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.8s4753×body1280valid
1.5s2136×body640valid
314.0ms701×body320valid
84.0ms273×body160valid
31.0ms10×body2560valid
26.0ms130×body80valid