Details

sample826.0ms

Algorithm

intervals

Results

576.0ms	166×	body	1280	valid
98.0ms	49×	body	640	valid
21.0ms	30×	body	320	valid
4.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify47.0ms

Counts: 1 → 1

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.7b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b	(cos (- lambda1 lambda2))

rewrite73.0ms

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:

21.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
30.0ms	(cos (- lambda1 lambda2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin phi1) (sin phi2))
66.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
41.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
30.0ms	(cos (- lambda1 lambda2))

simplify2.2s

Counts: 67 → 67

prune485.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
0.2b	(* (sin lambda1) (sin (- lambda2)))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite79.0ms

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` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 65

Calls

4 calls:

25.0ms	(* (sin phi1) (sin phi2))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
33.0ms	(* (sin lambda1) (sin (- lambda2)))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin phi1) (sin phi2))
124.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
83.0ms	(* (sin lambda1) (sin (- lambda2)))
48.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.1s

Counts: 77 → 77

prune759.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize65.0ms

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 lambda1) (sin (- lambda2)))
0.7b	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite69.0ms

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` `sin-neg` `log-pow` `distribute-rgt-neg-out` `sin-mult`

Counts

4 → 62

Calls

4 calls:

36.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
23.0ms	(* (sin lambda1) (sin (- lambda2)))
3.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (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)))))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
83.0ms	(* (sin lambda1) (sin (- lambda2)))
71.0ms	(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
25.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify1.1s

Counts: 74 → 74

prune774.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.6b

localize101.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(pow (* (sin phi1) (sin phi2)) 3)
1.0b	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
26.8b	(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite69.0ms

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` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `sin-neg` `*-commutative` `distribute-rgt-neg-out` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

33.0ms	(* (sin lambda1) (sin (- lambda2)))
18.0ms	(pow (* (sin phi1) (sin phi2)) 3)
5.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
9.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series319.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (sin lambda1) (sin (- lambda2)))
107.0ms	(pow (* (sin phi1) (sin phi2)) 3)
38.0ms	(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
74.0ms	(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify583.0ms

Counts: 81 → 81

prune689.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.6b

regimes1.0s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.8s

end0.0ms

sample18.2s

Algorithm

intervals

Results

12.7s	4788×	body	1280	valid
3.7s	2067×	body	640	valid
880.0ms	716×	body	320	valid
182.0ms	289×	body	160	valid
34.0ms	137×	body	80	valid
22.0ms	6×	body	2560	valid