Details

sample708.0ms

Algorithm

intervals

Results

391.0ms	147×	body	1280	valid
178.0ms	69×	body	640	valid
30.0ms	26×	body	320	valid
5.0ms	8×	body	160	valid
2.0ms	6×	body	80	valid

simplify86.0ms

Counts: 1 → 1

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.6b

localize535.0ms

Local error

Found 4 expressions with local error:

3.4b	(cos (- lambda1 lambda2))
0.8b	(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))

rewrite33.0ms

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

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

series163.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

69.0ms	(* (sin phi1) (sin phi2))
48.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
35.0ms	(cos (- lambda1 lambda2))
11.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify1.7s

Counts: 88 → 88

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.6b

localize70.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
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)
0.2b	(* (sin phi1) (sin phi2))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `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 → 76

Calls

4 calls:

Slowest

24.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
14.0ms	(* (sin phi1) (sin phi2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series212.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

79.0ms	(* (sin lambda1) (sin lambda2))
65.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
52.0ms	(* (sin phi1) (sin phi2))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify1.3s

Counts: 88 → 88

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.5b

localize129.0ms

Local error

Found 4 expressions with local error:

0.8b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))
0.5b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
0.2b	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) 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

19.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
5.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
4.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

68.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
42.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
16.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))
10.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))

simplify3.0s

Counts: 82 → 82

prune2.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize117.0ms

Local error

Found 4 expressions with local error:

9.5b	(cbrt (* (sin lambda1) (sin lambda2)))
9.5b	(cbrt (* (sin lambda1) (sin lambda2)))
9.5b	(cbrt (* (sin lambda1) (sin lambda2)))
0.8b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`
1×	`acos-asin`

Counts

4 → 50

Calls

4 calls:

Slowest

18.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
6.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
5.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

142.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
142.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
127.0ms	(cbrt (* (sin lambda1) (sin lambda2)))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (cbrt (* (sin lambda1) (sin lambda2))) (cbrt (* (sin lambda1) (sin lambda2)))) (cbrt (* (sin lambda1) (sin lambda2))))))))

simplify1.2s

Counts: 62 → 62

prune1.6s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.4b

regimes1.8s

Accuracy

0% (0.5b remaining)

Error of 3.8b against oracle of 3.3b and baseline of 3.8b

bsearch11.0ms

end0.0ms

sample24.5s

Algorithm

intervals

Results

16.9s	4798×	body	1280	valid
5.4s	2056×	body	640	valid
1.5s	712×	body	320	valid
235.0ms	302×	body	160	valid
57.0ms	9×	body	2560	valid
53.0ms	126×	body	80	valid