Details

sample671.0ms

Algorithm

intervals

Results

434.0ms	152×	body	1280	valid
81.0ms	63×	body	640	valid
19.0ms	24×	body	320	valid
5.0ms	9×	body	160	valid
2.0ms	8×	body	80	valid

simplify32.0ms

Counts

1 → 1

Iterations

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

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
0.2b	(* R (acos (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))))
3.4b	(cos (- lambda1 lambda2))

rewrite41.0ms

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:

0.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
10.0ms	(* R (acos (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))))
25.0ms	(cos (- lambda1 lambda2))

series291.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))
40.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1)))))
24.0ms	(acos (fma (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)) (* (sin phi2) (sin phi1))))
32.0ms	(cos (- lambda1 lambda2))

simplify3.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
4	4171
3	1268
2	509
1	293
0	168

prune967.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.9b

localize93.0ms

Local error

Found 4 expressions with local error:

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))
0.2b	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.1b	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

rewrite21.0ms

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:

0.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
13.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
1.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

series560.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))
89.0ms	(* (sin lambda1) (sin lambda2))
67.0ms	(* R (acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1)))))
26.0ms	(acos (fma (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))) (* (sin phi2) (sin phi1))))

simplify2.3s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	1711
2	598
1	258
0	127

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.8b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* R (log1p (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
0.5b	(expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
1.1b	(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

rewrite19.0ms

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:

10.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* R (log1p (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
0.0ms	(expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
1.0ms	(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

series358.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin lambda1) (sin lambda2))
173.0ms	(* R (log1p (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
76.0ms	(expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
36.0ms	(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

simplify5.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5000
4	3304
3	1334
2	481
1	214
0	118

prune1.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize106.0ms

Local error

Found 4 expressions with local error:

0.5b	(expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
0.7b	(log (exp (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
0.8b	(exp (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
1.1b	(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

1.0ms	(expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
4.0ms	(log (exp (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
2.0ms	(exp (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))
81.0ms	(log (exp (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2)))))))
137.0ms	(exp (expm1 (acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))))
25.0ms	(acos (fma (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin lambda2))) (* (cos phi2) (cos phi1)) (* (sin phi1) (sin phi2))))

simplify3.7s

Counts

65 → 65

Iterations

Iter	Nodes
done	5000
6	3191
5	1453
4	657
3	308
2	173
1	124
0	84

prune896.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 3.7b

regimes1.5s

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample18.6s

Algorithm

intervals

Results

12.0s	4761×	body	1280	valid
4.4s	2133×	body	640	valid
1.1s	685×	body	320	valid
233.0ms	281×	body	160	valid
36.0ms	134×	body	80	valid
33.0ms	7×	body	2560	valid