Details

sample619.0ms

Algorithm

intervals

Results

369.0ms	147×	body	1280	valid
145.0ms	65×	body	640	valid
23.0ms	30×	body	320	valid
4.0ms	8×	body	160	valid
1.0ms	6×	body	80	valid

simplify26.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	39
3	39
2	38
1	27
0	17

prune58.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 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)))
1.1b	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
3.2b	(cos (- lambda1 lambda2))

rewrite29.0ms

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` `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 → 61

Calls

4 calls:

6.0ms	(* R (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)))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
19.0ms	(cos (- lambda1 lambda2))

series392.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
259.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
21.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
58.0ms	(cos (- lambda1 lambda2))

simplify4.0s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	4360
3	1347
2	524
1	294
0	168

prune927.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.7b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* R (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	(* (sin lambda1) (sin lambda2))
1.2b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite18.0ms

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` `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 → 61

Calls

4 calls:

6.0ms	(* R (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)))
10.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
461.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
93.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1726
2	601
1	257
0	127

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.6b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* R (log1p (expm1 (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))))
0.5b	(expm1 (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
1.2b	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

rewrite43.0ms

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`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`acos-asin` `expm1-log1p` `sin-mult` `expm1-udef`

Counts

4 → 62

Calls

4 calls:

27.0ms	(* (sin phi1) (sin phi2))
12.0ms	(* R (log1p (expm1 (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))))
1.0ms	(expm1 (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sin phi1) (sin phi2))
126.0ms	(* R (log1p (expm1 (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))))
84.0ms	(expm1 (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
13.0ms	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

simplify4.8s

Counts

74 → 74

Iterations

Iter	Nodes
done	5002
5	4456
4	2218
3	941
2	393
1	195
0	107

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.5b

localize97.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))))
0.5b	(expm1 (exp (log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))))
0.6b	(log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
1.2b	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `log-prod`
5×	`add-exp-log` `log1p-expm1-u`
4×	`expm1-log1p-u` `exp-prod` `add-cbrt-cube` `add-log-exp`
3×	`exp-sum`
2×	`log-pow`
1×	`acos-asin` `expm1-log1p` `rem-log-exp` `expm1-udef` `rem-exp-log`

Counts

4 → 52

Calls

4 calls:

3.0ms	(exp (log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))))
0.0ms	(expm1 (exp (log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))))
1.0ms	(log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

series204.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(exp (log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))))
99.0ms	(expm1 (exp (log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))))
68.0ms	(log (acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2)))))
13.0ms	(acos (fma (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (cos phi1)) (cos phi2) (* (sin phi1) (sin phi2))))

simplify4.8s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
6	3200
5	1176
4	573
3	310
2	171
1	106
0	71

prune703.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.5b

regimes1.5s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample16.5s

Algorithm

intervals

Results

12.0s	4764×	body	1280	valid
3.2s	2102×	body	640	valid
611.0ms	699×	body	320	valid
183.0ms	288×	body	160	valid
59.0ms	13×	body	2560	valid
32.0ms	137×	body	80	valid