Details

sample1.0s

Algorithm

intervals

Results

617.0ms	152×	body	1280	valid
161.0ms	68×	body	640	valid
55.0ms	17×	body	320	valid
13.0ms	14×	body	160	valid
2.0ms	5×	body	80	valid

simplify87.0ms

Counts: 1 → 1

prune58.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.8b

localize66.0ms

Local error

Found 4 expressions with local error:

2.7b	(cos (- lambda1 lambda2))
1.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (sin phi1) (sin phi2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `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 → 76

Calls

4 calls:

Slowest

18.0ms	(* (sin phi1) (sin phi2))
12.0ms	(cos (- lambda1 lambda2))
11.0ms	(* (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)))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

67.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
67.0ms	(* (sin phi1) (sin phi2))
29.0ms	(cos (- lambda1 lambda2))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify2.4s

Counts: 88 → 88

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.3b

localize72.0ms

Local error

Found 4 expressions with local error:

1.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (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))
0.2b	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`cos-mult`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `associate-*l/`

Counts

4 → 84

Calls

4 calls:

Slowest

71.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
15.0ms	(* (sin phi1) (sin phi2))
11.0ms	(* (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))))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

267.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
112.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
81.0ms	(* (sin phi1) (sin phi2))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify916.0ms

Counts: 96 → 96

prune2.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

localize94.0ms

Local error

Found 4 expressions with local error:

1.9b	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))
0.7b	(log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
0.2b	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`pow1`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`log-prod` `associate-l`
6×	`associate-r`
4×	`expm1-log1p-u` `exp-sum` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `fma-udef` `unswap-sqr`
1×	`distribute-rgt-in` `acos-asin` `distribute-lft-in` `rem-log-exp` `associate-*l/` `log-pow` `cos-mult`

Counts

4 → 75

Calls

4 calls:

Slowest

38.0ms	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
23.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))
2.0ms	(log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
1.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

317.0ms	(* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))
91.0ms	(* (exp (log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
59.0ms	(log (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
19.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

simplify1.7s

Counts: 87 → 87

prune2.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize85.0ms

Local error

Found 4 expressions with local error:

1.9b	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))
1.2b	(log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))))
0.3b	(exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
0.2b	(* (log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `rem-exp-log`

Counts

4 → 70

Calls

4 calls:

Slowest

17.0ms	(* (log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
6.0ms	(log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))))
6.0ms	(exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
2.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))

series119.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

62.0ms	(* (log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))) R)
36.0ms	(exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1)))))))
11.0ms	(acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))
11.0ms	(log (exp (acos (fma (sin phi2) (sin phi1) (* (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))))))))

simplify4.1s

Counts: 82 → 82

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.1b

regimes1.4s

Accuracy

0% (0.5b remaining)

Error of 3.9b against oracle of 3.4b and baseline of 3.9b

bsearch20.0ms

end0.0ms

sample24.3s

Algorithm

intervals

Results

16.5s	4795×	body	1280	valid
5.9s	2091×	body	640	valid
991.0ms	678×	body	320	valid
245.0ms	270×	body	160	valid
97.0ms	158×	body	80	valid
62.0ms	9×	body	2560	valid