Details

sample706.0ms

Algorithm

intervals

Results

413.0ms	140×	body	1280	valid
169.0ms	70×	body	640	valid
28.0ms	32×	body	320	valid
5.0ms	8×	body	160	valid
1.0ms	6×	body	80	valid

simplify155.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (51.0ms)

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

prune121.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize42.0ms

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)
0.9b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.5b	(cos (- lambda1 lambda2))

rewrite86.0ms

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:

52.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(* (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)))))
21.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
91.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
13.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
32.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

86 → 86

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	196	1763
1	400	1595
2	1597	1331
done	5000	1299

prune639.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.4b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.8b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite133.0ms

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:

88.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
25.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
78.0ms	(* (sin lambda1) (sin lambda2))
120.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
20.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify953.0ms

Counts

90 → 90

Iterations

Useful iterations: done (950.0ms)

Iter	Nodes	Cost
0	143	2023
1	317	1963
2	1318	1477
done	5000	1429

prune785.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
0.5b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
0.8b	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

rewrite35.0ms

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:

26.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
2.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
4.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))) R)
59.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))
14.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))))
24.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))

simplify2.2s

Counts

78 → 78

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	93	2330
1	149	2225
2	409	1971
3	2376	1971
done	5000	1971

prune696.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
0.3b	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))) R)
0.5b	(asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
0.7b	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
51×	`*-un-lft-identity`
47×	`add-cube-cbrt`
39×	`prod-diff`
38×	`times-frac`
13×	`fma-neg`
6×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`associate-r`
2×	`asin-acos` `flip3--` `associate-*l/` `flip--` `distribute-lft-out--`
1×	`sub-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `associate--r-` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

1.0ms	(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
86.0ms	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))) R)
1.0ms	(asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
49.0ms	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

425.0ms	(fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))
221.0ms	(* (- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))) R)
21.0ms	(asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2))))
92.0ms	(- (/ PI 2) (asin (fma (* (cos phi1) (cos phi2)) (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (* (sin phi1) (sin phi2)))))

simplify2.0s

Counts

127 → 127

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	194	8844
1	413	5942
2	1508	4708
done	5000	3694

prune938.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.1b

regimes1.5s

Accuracy

0% (0.8b remaining)

Error of 4.2b against oracle of 3.5b and baseline of 4.2b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

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

end0.0ms

sample16.6s

Algorithm

intervals

Results

11.9s	4792×	body	1280	valid
3.3s	2087×	body	640	valid
608.0ms	696×	body	320	valid
126.0ms	283×	body	160	valid
39.0ms	8×	body	2560	valid
31.0ms	139×	body	80	valid