Details

sample637.0ms

Algorithm

intervals

Results

378.0ms	154×	body	1280	valid
144.0ms	71×	body	640	valid
14.0ms	20×	body	320	valid
4.0ms	7×	body	160	valid
3.0ms	1×	body	2560	valid
1.0ms	3×	body	80	valid

simplify5.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.4b	(cos (- lambda1 lambda2))

rewrite51.0ms

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:

7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms	(* (sin phi1) (sin phi2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
27.0ms	(cos (- lambda1 lambda2))

series195.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
58.0ms	(* (sin phi1) (sin phi2))
26.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
41.0ms	(cos (- lambda1 lambda2))

simplify90.0ms

Counts: 67 → 67

prune520.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.5b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite163.0ms

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:

131.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
12.0ms	(* (sin phi1) (sin phi2))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

316.0ms	(* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
113.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
55.0ms	(* (sin phi1) (sin phi2))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify58.0ms

Counts: 88 → 88

prune766.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.3b

localize64.0ms

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))))))))) R)
0.2b	(* (sin phi1) (sin phi2))
0.6b	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `associate-l`
8×	`add-exp-log` `add-cbrt-cube`
7×	`log-prod`
6×	`associate-r`
4×	`exp-sum` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`acos-asin` `rem-log-exp` `log-pow` `sin-mult`

Counts

4 → 61

Calls

4 calls:

27.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
12.0ms	(* (sin phi1) (sin phi2))
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)))))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
84.0ms	(* (sin phi1) (sin phi2))
95.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
20.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify87.0ms

Counts: 73 → 73

prune783.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.7b	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite504.0ms

Algorithm

rewrite-expression-head

Rules

58×	`cos-mult`
45×	`pow1`
38×	`sin-mult`
37×	`associate-*r/`
33×	`frac-times` `associate-/l/`
27×	`add-exp-log` `add-cbrt-cube`
22×	`associate-*l/`
18×	`pow-prod-down` `frac-sub`
12×	`prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `sub-div`
8×	`add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-/r*` `associate-/r/`
2×	`flip3--` `pow-plus` `*-commutative` `flip--`
1×	`pow2` `acos-asin` `frac-2neg` `flip3-+` `swap-sqr` `frac-add` `clear-num` `flip-+` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

13.0ms	(* (sin phi1) (sin phi2))
428.0ms	(/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
53.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin phi1) (sin phi2))
810.0ms	(/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
70.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
73.0ms	(acos (+ (* (sin phi1) (sin phi2)) (/ (* (* (cos phi1) (cos phi2)) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2)))))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify110.0ms

Counts: 135 → 135

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

regimes974.0ms

Accuracy

4.1% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify75.0ms

end0.0ms

sample17.9s

Algorithm

intervals

Results

12.5s	4713×	body	1280	valid
3.6s	2154×	body	640	valid
822.0ms	695×	body	320	valid
143.0ms	290×	body	160	valid
75.0ms	136×	body	80	valid
69.0ms	13×	body	2560	valid