Details

sample1.9s

Algorithm

intervals

Results

763.0ms	158×	body	1280	valid
204.0ms	64×	body	640	valid
21.0ms	14×	body	320	valid
12.0ms	15×	body	160	valid
7.0ms	1×	body	2560	valid
2.0ms	5×	body	80	valid

simplify88.0ms

Counts: 1 → 1

prune75.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize95.0ms

Local error

Found 4 expressions with local error:

3.2b	(cos (- lambda1 lambda2))
1.4b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
0.3b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))

rewrite33.0ms

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`

Counts

4 → 65

Calls

4 calls:

Slowest

11.0ms	(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)))

series529.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

411.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
53.0ms	(cos (- lambda1 lambda2))
46.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
19.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))

simplify1.5s

Counts: 77 → 77

prune1.8s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize109.0ms

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	(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 phi2) (sin phi1))

rewrite37.0ms

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`

Counts

4 → 65

Calls

4 calls:

Slowest

22.0ms	(* (sin phi2) (sin phi1))
12.0ms	(* 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)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

394.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
69.0ms	(* (sin phi2) (sin phi1))
51.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
20.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.6s

Counts: 77 → 77

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.7b

localize137.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
0.2b	(* R (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
0.2b	(exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

Slowest

13.0ms	(* R (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
3.0ms	(exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))
1.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

57.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
33.0ms	(* R (exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
25.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))
10.0ms	(exp (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))))

simplify1.6s

Counts: 81 → 81

prune2.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 3.7b

localize98.0ms

Local error

Found 4 expressions with local error:

1.4b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))
0.7b	(log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
0.6b	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
0.2b	(* R (exp (log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

Slowest

10.0ms	(* R (exp (log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))))
1.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))
0.0ms	(log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

151.0ms	(* R (exp (log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))))
104.0ms	(log1p (expm1 (log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))))
35.0ms	(log (acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2)))))))
10.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi2) (cos phi1)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))))))

simplify4.0s

Counts: 71 → 71

prune2.2s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 3.6b

regimes1.8s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch7.0ms

end0.0ms

sample23.0s

Algorithm

intervals

Results

16.3s	4747×	body	1280	valid
4.7s	2117×	body	640	valid
1.4s	698×	body	320	valid
216.0ms	292×	body	160	valid
79.0ms	139×	body	80	valid
54.0ms	8×	body	2560	valid