Details

sample822.0ms

Algorithm

intervals

Results

387.0ms	147×	body	1280	valid
199.0ms	69×	body	640	valid
90.0ms	25×	body	320	valid
6.0ms	10×	body	160	valid
2.0ms	6×	body	80	valid

simplify37.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	17	19
1	27	18
2	38	18
3	44	18
4	46	18
done	46	18

prune60.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
0.8b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b	(cos (- lambda1 lambda2))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log`
9×	`prod-diff`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

49.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
16.0ms	(cos (- lambda1 lambda2))

series292.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
54.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))))
22.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
45.0ms	(cos (- lambda1 lambda2))

simplify821.0ms

Counts

86 → 86

Iterations

Useful iterations: done (817.0ms)

Iter	Nodes	Cost
0	195	1763
1	401	1595
2	1502	1333
done	5000	1299

prune767.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.3b

localize66.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

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` `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 → 80

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
69.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
10.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin lambda1) (sin lambda2))
296.0ms	(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
44.0ms	(* R (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
23.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify2.0s

Counts

92 → 92

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	179	2086
1	496	1975
2	2716	1732
done	5001	1725

prune1.0s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)
0.8b	(acos (fma (sin phi1) (sin phi2) (/ (* (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3)) (* (cos phi1) (cos phi2))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
22×	`add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down`
10×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `pow-unpow` `*-un-lft-identity` `add-cube-cbrt`
5×	`cos-mult`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `sqr-pow`
1×	`pow2` `acos-asin` `frac-times` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `*-commutative` `sin-mult`

Counts

4 → 99

Calls

4 calls:

7.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
49.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
1.0ms	(acos (fma (sin phi1) (sin phi2) (/ (* (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3)) (* (cos phi1) (cos phi2))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
97.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
96.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
78.0ms	(acos (fma (sin phi1) (sin phi2) (/ (* (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3)) (* (cos phi1) (cos phi2))) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (- (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))) (* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify1.9s

Counts

111 → 111

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	180	2064
1	554	1663
2	3165	1424
done	5001	1423

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

localize144.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2))))))
0.5b	(log (exp (acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2)))))))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)
0.8b	(acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cube-cbrt`
7×	`add-cbrt-cube` `add-exp-log`
6×	`exp-prod`
5×	`add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`acos-asin` `pow-unpow` `log-prod`
2×	`pow-pow` `exp-diff` `pow-exp` `rem-cube-cbrt`
1×	`cube-div` `cube-mult` `pow-to-exp` `log-div` `unpow-prod-down` `unpow3` `cube-prod` `rem-log-exp` `pow-prod-down` `prod-exp` `cos-mult` `cbrt-unprod` `sqr-pow` `rem-exp-log`

Counts

4 → 67

Calls

4 calls:

2.0ms	(exp (acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2))))))
2.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2)))))))
7.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
1.0ms	(acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2)))))

series727.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(exp (acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2))))))
54.0ms	(log (exp (acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2)))))))
510.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)
43.0ms	(acos (fma (sin phi1) (sin phi2) (/ (* (* (cos phi1) (cos phi2)) (+ (pow (* (cos lambda1) (cos lambda2)) 3) (pow (* (sin lambda1) (sin lambda2)) 3))) (fma (* (sin lambda1) (sin lambda2)) (- (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))) (pow (* (cos lambda1) (cos lambda2)) 2)))))

simplify659.0ms

Counts

79 → 79

Iterations

Useful iterations: done (654.0ms)

Iter	Nodes	Cost
0	134	3592
1	326	3468
2	1184	3091
done	5000	3090

prune940.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

regimes1.1s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	28
1	28	28
done	28	28

end0.0ms

sample19.0s

Algorithm

intervals

Results

14.0s	4775×	body	1280	valid
3.3s	2113×	body	640	valid
706.0ms	687×	body	320	valid
195.0ms	281×	body	160	valid
71.0ms	133×	body	80	valid
56.0ms	12×	body	2560	valid