Details

sample988.0ms

Algorithm

intervals

Results

678.0ms	163×	body	1280	valid
191.0ms	55×	body	640	valid
29.0ms	24×	body	320	valid
8.0ms	9×	body	160	valid
2.0ms	5×	body	80	valid

simplify67.0ms

Calls

1 calls:

Slowest

66.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.3b

localize49.0ms

Local error

Found 4 expressions with local error:

2.3b	(cos (- lambda1 lambda2))
1.4b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.3b	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
0.2b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
9×	`prod-diff`
6×	`pow1` `add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`acos-asin` `cos-diff` `sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Calls

4 calls:

Slowest

12.0ms	(cos (- lambda1 lambda2))
6.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))

series335.0ms

Calls

4 calls:

Slowest

255.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
41.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
28.0ms	(cos (- lambda1 lambda2))
10.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify2.6s

Calls

34 calls:

Slowest

450.0ms	(+ (* (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2))) (* (sin phi1) (sin phi2)))
425.0ms	(* (* (* R R) R) (* (* (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))) (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))) (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))
131.0ms	(- (+ 1 (* lambda2 lambda1)) (* 1/2 (pow lambda1 2)))
122.0ms	(- (+ (* phi1 phi2) 1) (* 1/2 (pow phi1 2)))
96.0ms	(* (sqrt R) (sqrt (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize82.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
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` `fma-udef` `sin-mult`

Calls

4 calls:

Slowest

17.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
2.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))
0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))

series509.0ms

Calls

4 calls:

Slowest

379.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
76.0ms	(* (sin lambda1) (sin lambda2))
38.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
16.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify6.1s

Calls

33 calls:

Slowest

414.0ms	(* (acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))) R)
400.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda2) (sin lambda1)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
372.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
366.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
365.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.1b

localize94.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))
0.2b	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`associate-l`
15×	`add-exp-log`
14×	`*-un-lft-identity`
13×	`pow1` `add-cbrt-cube`
12×	`associate-r` `add-cube-cbrt`
9×	`unswap-sqr`
7×	`prod-exp`
5×	`pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sin-mult`
1×	`acos-asin` `1-exp`

Calls

4 calls:

Slowest

28.0ms	(* (sin phi1) (sin phi2))
24.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

series191.0ms

Calls

4 calls:

Slowest

72.0ms	(* (sin phi1) (sin phi2))
51.0ms	(* (sin lambda1) (sin lambda2))
50.0ms	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
19.0ms	(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))

simplify7.8s

Calls

59 calls:

Slowest

459.0ms	(+ (log (* R 1)) (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
406.0ms	(* (* (sqrt R) (sqrt 1)) (sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2))))))
405.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
369.0ms	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))
360.0ms	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2)))) (cos phi1) (* (sin phi1) (sin phi2)))))

prune2.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.1b

localize74.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2))))
0.2b	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2)))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (sin phi1) (sin phi2))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
22×	`associate-l`
15×	`add-exp-log`
14×	`*-un-lft-identity`
13×	`pow1` `add-cbrt-cube`
12×	`associate-r` `add-cube-cbrt`
9×	`unswap-sqr`
7×	`prod-exp`
5×	`pow-prod-down` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sin-mult`
1×	`acos-asin` `1-exp`

Calls

4 calls:

Slowest

27.0ms	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2)))))
24.0ms	(* (sin lambda1) (sin lambda2))
24.0ms	(* (sin phi1) (sin phi2))
8.0ms	(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2))))

series213.0ms

Calls

4 calls:

Slowest

75.0ms	(* (sin phi1) (sin phi2))
60.0ms	(* (sin lambda1) (sin lambda2))
58.0ms	(* (* R 1) (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2)))))
20.0ms	(acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2))))

simplify8.2s

Calls

59 calls:

Slowest

400.0ms	(* (sqrt (* R 1)) (sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2))))))
400.0ms	(+ (log (* R 1)) (log (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2))))))
387.0ms	(* (sqrt (* R 1)) (sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2))))))
385.0ms	(* (* (* (sin phi1) (sin phi1)) (sin phi1)) (* (* (sin phi2) (sin phi2)) (sin phi2)))
373.0ms	(* (* (sqrt R) 1) (sqrt (acos (fma (* (cos phi2) (fma (cos lambda2) (cos lambda1) (expm1 (log1p (* (sin lambda1) (sin lambda2)))))) (cos phi1) (* (sin phi1) (sin phi2))))))

prune2.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.1b

regimes1.5s

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch4.0ms

end0.0ms

sample24.3s

Algorithm

intervals

Results

17.8s	4822×	body	1280	valid
4.9s	2070×	body	640	valid
896.0ms	671×	body	320	valid
295.0ms	295×	body	160	valid
69.0ms	12×	body	2560	valid
49.0ms	130×	body	80	valid