Details

sample836.0ms

Algorithm

intervals

Results

494.0ms	156×	body	1280	valid
199.0ms	71×	body	640	valid
22.0ms	20×	body	320	valid
4.0ms	6×	body	160	valid
1.0ms	3×	body	80	valid

simplify109.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (14.0ms)

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

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.5b

localize77.0ms

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)
0.5b	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.4b	(cos (- lambda1 lambda2))

rewrite144.0ms

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:

87.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(* (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)))))
35.0ms	(cos (- lambda1 lambda2))

series376.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
101.0ms	(* (acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
23.0ms	(acos (fma (sin phi1) (sin phi2) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
50.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

86 → 86

Iterations

Useful iterations: done (1.6s)

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

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.3b

localize107.0ms

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 lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.6b	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite151.0ms

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))
105.0ms	(* (* (cos phi1) (cos phi2)) (* (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)
1.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sin lambda1) (sin lambda2))
212.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
148.0ms	(* (acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
37.0ms	(acos (fma (sin phi1) (sin phi2) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify1.3s

Counts

90 → 90

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	143	2023
1	318	1963
2	1331	1477
done	5001	1429

prune1.3s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.1b

localize108.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.3b	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))) R)
0.6b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2))))
0.8b	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

27.0ms	(* (sin lambda2) (sin lambda1))
54.0ms	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))) R)
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2))))
3.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))

series298.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin lambda2) (sin lambda1))
111.0ms	(* (exp (log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))) R)
26.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2))))
78.0ms	(log (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))

simplify5.8s

Counts

81 → 81

Iterations

Useful iterations: done (5.8s)

Iter	Nodes	Cost
0	119	1949
1	211	1882
2	615	1636
3	3912	1634
done	5001	1632

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 2.1b

localize113.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (exp (log (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))))) R)
0.6b	(expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))
0.6b	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2))))
0.8b	(log (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

36.0ms	(* (exp (log (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))))) R)
1.0ms	(expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))
13.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2))))
3.0ms	(log (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(* (exp (log (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))))) R)
95.0ms	(expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))
22.0ms	(acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2))))
158.0ms	(log (log1p (expm1 (acos (fma (* (cos phi1) (cos phi2)) (fma (cos lambda2) (cos lambda1) (* (sin lambda2) (sin lambda1))) (* (sin phi1) (sin phi2)))))))

simplify9.1s

Counts

71 → 71

Iterations

Useful iterations: done (9.1s)

Iter	Nodes	Cost
0	100	2259
1	163	2089
2	506	1815
3	3881	1815
done	5001	1813

prune1.0s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.1b

regimes2.5s

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	30
1	30	30
done	30	30

end0.0ms

sample23.8s

Algorithm

intervals

Results

16.1s	4780×	body	1280	valid
4.9s	2104×	body	640	valid
1.4s	729×	body	320	valid
172.0ms	256×	body	160	valid
49.0ms	124×	body	80	valid
49.0ms	9×	body	2560	valid