Details

sample579.0ms

Algorithm

intervals

Results

292.0ms	144×	body	1280	valid
125.0ms	76×	body	640	valid
15.0ms	19×	body	320	valid
6.0ms	12×	body	160	valid
3.0ms	1×	body	2560	valid
1.0ms	4×	body	80	valid

simplify79.0ms

Counts

1 → 1

Iterations

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

prune60.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize94.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.9b	(cos (- lambda1 lambda2))
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

rewrite104.0ms

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` `insert-posit16` `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 → 78

Calls

4 calls:

52.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(cos (- lambda1 lambda2))
15.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series761.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
309.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
49.0ms	(cos (- lambda1 lambda2))
85.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify7.0s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
3	3407
2	956
1	406
0	201

prune2.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.1b

localize211.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `cos-mult` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-l/` `associate-r/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

78.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
88.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
9.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
3.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
313.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
380.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
83.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify3.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1494
1	436
0	178

prune2.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 5.9b

localize119.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
0.3b	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
0.7b	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
2.0b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

2.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
29.0ms	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
2.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

series1.5s

Counts

4 → 12

Calls

4 calls:

772.0ms	(fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))
370.0ms	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
258.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
118.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

simplify8.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
4	4211
3	1270
2	500
1	215
0	121

prune2.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.9b

localize163.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
0.4b	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
1.3b	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))
2.0b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-cbrt-cube` `add-exp-log`
5×	`add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `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` `unswap-sqr` `rem-exp-log`

Counts

4 → 70

Calls

4 calls:

38.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
7.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
10.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))
3.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(* (log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))) R)
188.0ms	(exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1)))))
87.0ms	(log (exp (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))))
81.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda2) (sin lambda1))) (* (sin phi2) (sin phi1))))

simplify6.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
5	2750
4	1820
3	1045
2	364
1	166
0	107

prune1.7s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 5.9b

regimes6.3s

Accuracy

0% (0.5b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample18.7s

Algorithm

intervals

Results

13.3s	4823×	body	1280	valid
3.4s	2129×	body	640	valid
1.0s	633×	body	320	valid
135.0ms	257×	body	160	valid
101.0ms	147×	body	80	valid
58.0ms	12×	body	2560	valid