Details

Time bar (total: 12.0s)

sample287.0ms

Algorithm
intervals
Results
195.0ms146×body1280valid
53.0ms75×body640valid
12.0ms23×body320valid
3.0ms10×body160valid
0.0ms2×body80valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612
done3612

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize35.0ms

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)))))
4.9b
(cos (- lambda1 lambda2))

rewrite31.0ms

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*
4×add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 55
Calls
4 calls:
11.0ms
(* (sin phi1) (sin phi2))
6.0ms
(* (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)))))
10.0ms
(cos (- lambda1 lambda2))

series132.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin phi1) (sin phi2))
51.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
20.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21790569
35001569
done5001569

prune303.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize31.0ms

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)) (* (sin lambda1) (sin lambda2)))))) R)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite32.0ms

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:
11.0ms
(* (sin phi1) (sin phi2))
11.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* (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))))))

series188.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin phi1) (sin phi2))
45.0ms
(* (sin lambda1) (sin lambda2))
73.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
20.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify74.0ms

Counts
76 → 76
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0260929
1831774
21930774
33056774
45001774
done5001774

prune387.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
0.2b
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.7b
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt log-prod *-un-lft-identity
8×pow1
7×exp-sum
6×add-exp-log associate-*l* add-cbrt-cube
4×exp-prod add-log-exp
3×associate-*r*
2×log-pow unswap-sqr
1×acos-asin rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Counts
4 → 57
Calls
4 calls:
3.0ms
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
17.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series170.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
77.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
55.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify156.0ms

Counts
69 → 69
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
01741588
13951344
28181299
312161293
428531293
550011293
done50011293

prune407.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
0.3b
(pow (* (sin lambda1) (sin lambda2)) 3)
1.4b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
26.6b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite25.0ms

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:
9.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
8.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
4.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series212.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
70.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
18.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
46.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify184.0ms

Counts
79 → 79
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
02851038
11031891
24820891
35001891
done5001891

prune356.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.7b

regimes906.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03421
13421
done3421

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.7s4712×body1280valid
1.4s2171×body640valid
306.0ms695×body320valid
78.0ms291×body160valid
33.0ms11×body2560valid
17.0ms121×body80valid