Details

sample866.0ms

Algorithm

intervals

Results

531.0ms	149×	body	1280	valid
140.0ms	74×	body	640	valid
35.0ms	24×	body	320	valid
3.0ms	3×	body	160	valid
3.0ms	6×	body	80	valid

simplify90.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

89.0ms

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

prune57.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.1b

localize85.0ms

Local error

Found 4 expressions with local error:

3.0b	(cos (- lambda1 lambda2))
0.6b	(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))

rewrite72.0ms

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

22.0ms	(* (sin phi1) (sin phi2))
21.0ms	(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)))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

65.0ms	(* (sin phi1) (sin phi2))
59.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
32.0ms	(cos (- lambda1 lambda2))
12.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify2.2s

Counts

44 → 88

Calls

44 calls:

Slowest

438.0ms	(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))) (* (* R R) R))
393.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
152.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
78.0ms	(* (cos (fma (* (cbrt lambda1) (cbrt lambda1)) (cbrt lambda1) (- (* lambda2 1)))) (cos (fma (- lambda2) 1 (* lambda2 1))))
73.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.2b

localize92.0ms

Local error

Found 4 expressions with local error:

0.6b	(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	(* (sin lambda1) (sin lambda2))

rewrite42.0ms

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

13.0ms	(* (sin phi1) (sin phi2))
12.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
12.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series284.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

95.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
86.0ms	(* (sin phi1) (sin phi2))
79.0ms	(* (sin lambda1) (sin lambda2))
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify5.1s

Counts

43 → 88

Calls

43 calls:

Slowest

377.0ms	(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
365.0ms	(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))
353.0ms	(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
345.0ms	(+ (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (log R))
342.0ms	(* (sqrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) (sqrt R))

prune2.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 3.0b

localize83.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (exp (* (sin lambda1) (sin lambda2))))
0.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.2b	(* (sin phi1) (sin phi2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

Slowest

17.0ms	(* (sin phi1) (sin phi2))
6.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
5.0ms	(log (exp (* (sin lambda1) (sin lambda2))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

85.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
63.0ms	(* (sin phi1) (sin phi2))
59.0ms	(log (exp (* (sin lambda1) (sin lambda2))))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

simplify4.9s

Counts

38 → 83

Calls

38 calls:

Slowest

708.0ms	(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
387.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
353.0ms	(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
344.0ms	(* (* (* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (* (* R R) R))
325.0ms	(* (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (cbrt (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))))

prune2.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.0b

localize82.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (exp (* (sin lambda1) (sin lambda2))))
2.3b	(log (exp (* (sin phi1) (sin phi2))))
0.6b	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
0.2b	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

Slowest

12.0ms	(log (exp (* (sin lambda1) (sin lambda2))))
8.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
5.0ms	(log (exp (* (sin phi1) (sin phi2))))
3.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

series268.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

95.0ms	(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
81.0ms	(log (exp (* (sin phi1) (sin phi2))))
64.0ms	(log (exp (* (sin lambda1) (sin lambda2))))
28.0ms	(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

simplify4.4s

Counts

33 → 78

Calls

33 calls:

Slowest

343.0ms	(* (* (* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (* (* R R) R))
318.0ms	(* R (acos (+ (* (cos phi1) (* (cos phi2) (* (sin lambda1) (sin lambda2)))) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (sin phi1) (sin phi2))))))
316.0ms	(* (sqrt (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (sqrt R))
312.0ms	(* (sqrt (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))) (sqrt R))
310.0ms	(sqrt (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))))

prune2.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.0b

regimes2.3s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch9.0ms

end0.0ms

sample24.4s

Algorithm

intervals

Results

16.9s	4891×	body	1280	valid
5.3s	2033×	body	640	valid
1.5s	661×	body	320	valid
267.0ms	278×	body	160	valid
50.0ms	131×	body	80	valid
47.0ms	8×	body	2560	valid