Details

Time bar (total: 22.0s)

sample257.0ms

Algorithm
intervals
Results
183.0ms154×body1280valid
41.0ms66×body640valid
10.0ms25×body320valid
2.0ms8×body160valid
0.0ms3×body80valid

simplify20.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
01719
12718
23818
34318
done4318

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.6b
(cos (- lambda1 lambda2))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×cos-sum
9×prod-diff
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 72
Calls
4 calls:
12.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms
(cos (- lambda1 lambda2))

series125.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin phi1) (sin phi2))
50.0ms
(* (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)))))
18.0ms
(cos (- lambda1 lambda2))

simplify3.1s

Counts
84 → 84
Iterations

Useful iterations: 5 (1.1s)

IterNodesCost
01871607
13161393
25971170
39421127
412471054
51907990
63847990
done5001990

prune377.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.5b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite37.0ms

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×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 72
Calls
4 calls:
14.0ms
(* (sin lambda1) (sin lambda2))
12.0ms
(* (sin phi1) (sin phi2))
7.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series187.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin lambda1) (sin lambda2))
46.0ms
(* (sin phi1) (sin phi2))
73.0ms
(* (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))))))

simplify2.7s

Counts
84 → 84
Iterations

Useful iterations: 2 (104.0ms)

IterNodesCost
01411538
12711441
26991225
313391225
418091225
527431225
done50011225

prune502.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.6b

localize35.0ms

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)
1.5b
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
27.1b
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite24.0ms

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×expm1-log1p-u log1p-expm1-u 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 → 75
Calls
4 calls:
7.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
9.0ms
(pow (* (sin phi1) (sin phi2)) 3)
3.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series218.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(* (acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
73.0ms
(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))))))
51.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify2.2s

Counts
87 → 87
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01421840
13011556
28771310
336671309
done50001305

prune532.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 4.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b
(fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))
0.3b
(* (exp (log (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))))) R)
0.6b
(log (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))))
1.5b
(acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
7×pow1 log-prod
6×add-exp-log associate-*l* add-cbrt-cube
4×expm1-log1p-u exp-sum log1p-expm1-u add-log-exp
3×associate-*r*
2×unswap-sqr
1×acos-asin rem-log-exp pow-prod-down prod-exp log-pow *-commutative cbrt-unprod fma-udef
Counts
4 → 58
Calls
4 calls:
0.0ms
(fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))
18.0ms
(* (exp (log (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))))) R)
1.0ms
(log (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))))
1.0ms
(acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))
52.0ms
(* (exp (log (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))))) R)
41.0ms
(log (acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1)))))
12.0ms
(acos (fma (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))) (* (cos phi1) (cos phi2)) (* (sin phi2) (sin phi1))))

simplify1.9s

Counts
70 → 70
Iterations

Useful iterations: 4 (862.0ms)

IterNodesCost
01102124
11862056
24151773
310121772
436791769
done50001769

prune396.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 4.6b

regimes797.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.6b and baseline of 3.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02529
13329
done3329

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.6s4776×body1280valid
1.5s2013×body640valid
310.0ms759×body320valid
77.0ms288×body160valid
55.0ms16×body2560valid
22.0ms151×body80valid