Details

sample649.0ms

Algorithm

intervals

Results

432.0ms	152×	body	1280	valid
88.0ms	70×	body	640	valid
20.0ms	25×	body	320	valid
5.0ms	9×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	17	19
1	29	18
2	42	18
3	46	18
done	46	18

prune65.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.3b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.6b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.1b	(cos (- lambda1 lambda2))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1` `add-exp-log` `cos-sum` `add-cbrt-cube`
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:

81.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
31.0ms	(cos (- lambda1 lambda2))

series246.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
55.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
12.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
37.0ms	(cos (- lambda1 lambda2))

simplify2.7s

Counts

86 → 86

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	196	1763
1	754	1535
done	5000	1325

prune659.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.3b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.6b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `sin-mult`
2×	`cos-mult` `unswap-sqr`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 78

Calls

4 calls:

25.0ms	(* (sin lambda1) (sin lambda2))
102.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
14.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin lambda1) (sin lambda2))
182.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
104.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
35.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify10.9s

Counts

90 → 90

Iterations

Useful iterations: 2 (7.2s)

Iter	Nodes	Cost
0	143	2023
1	546	1773
2	4219	1429
done	5002	1429

prune875.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.2b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
1.6b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
27.7b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-r` `associate-l`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `cbrt-div` `pow1/3` `*-commutative` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

13.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
7.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
1.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
5.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series695.0ms

Counts

4 → 12

Calls

4 calls:

493.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
121.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
20.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
62.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify1.7s

Counts

87 → 87

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	138	2024
1	655	1546
done	5001	1310

prune819.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 4.2b

localize85.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
0.3b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
1.2b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
1.6b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`expm1-log1p-u` `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` `rem-exp-log` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

18.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
4.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
6.0ms	(log (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))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))) R)
85.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2)))))
26.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))))
15.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (sin phi1) (sin phi2))))

simplify4.0s

Counts

78 → 78

Iterations

Useful iterations: 2 (296.0ms)

Iter	Nodes	Cost
0	93	2330
1	236	2200
2	962	1971
done	5000	1971

prune557.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 4.2b

regimes1.9s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	34
1	32	34
done	32	34

end0.0ms

sample19.9s

Algorithm

intervals

Results

13.9s	4768×	body	1280	valid
3.8s	2136×	body	640	valid
1.1s	682×	body	320	valid
197.0ms	266×	body	160	valid
64.0ms	13×	body	2560	valid
46.0ms	136×	body	80	valid